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← 4-1 · Use the 180-degree line to find figure angles · Angle Facts in a Figure

Use the 180-degree line to find figure angles · 8 practice problems

4.MD.C.74.G.A.1

Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 70 degrees

Find the measure of angle x.

80° 100° 70° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 80 degrees, upper-left 100 degrees, and bottom-right 70 degrees. The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 80 degrees.
  • Upper-left inside angle = 100 degrees.
  • Bottom-right inside angle = 70 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−80∘−100∘−70∘=110∘360^\circ - 80^\circ - 100^\circ - 70^\circ = 110^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (110 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−110∘=70∘180^\circ - 110^\circ = 70^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 70 degrees

Review

80 + 100 + 70 + 110 = 360 degrees, a valid quadrilateral. And 110 + 70 = 180 degrees fills the straight line. The marked angle 70 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 70 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!
Variant 2 answer: 70 degrees

Find the measure of angle x.

70° 95° 85° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 70 degrees, upper-left 95 degrees, and bottom-right 85 degrees. The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 70 degrees.
  • Upper-left inside angle = 95 degrees.
  • Bottom-right inside angle = 85 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−70∘−95∘−85∘=110∘360^\circ - 70^\circ - 95^\circ - 85^\circ = 110^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (110 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−110∘=70∘180^\circ - 110^\circ = 70^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 70 degrees

Review

70 + 95 + 85 + 110 = 360 degrees, a valid quadrilateral. And 110 + 70 = 180 degrees fills the straight line. The marked angle 70 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 70 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!
Variant 3 answer: 90 degrees

Find the measure of angle x.

90° 90° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 90 degrees, upper-left 90 degrees, and bottom-right 90 degrees (a right angle on the line). The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 90 degrees.
  • Upper-left inside angle = 90 degrees.
  • Bottom-right inside angle = 90 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−90∘−90∘−90∘=90∘360^\circ - 90^\circ - 90^\circ - 90^\circ = 90^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (90 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−90∘=90∘180^\circ - 90^\circ = 90^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 90 degrees

Review

90 + 90 + 90 + 90 = 360 degrees, a valid quadrilateral. And 90 + 90 = 180 degrees fills the straight line. The marked angle 90 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 90 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!
Variant 4 answer: 90 degrees

Find the measure of angle x.

55° 120° 95° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 55 degrees, upper-left 120 degrees, and bottom-right 95 degrees. The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 55 degrees.
  • Upper-left inside angle = 120 degrees.
  • Bottom-right inside angle = 95 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−55∘−120∘−95∘=90∘360^\circ - 55^\circ - 120^\circ - 95^\circ = 90^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (90 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−90∘=90∘180^\circ - 90^\circ = 90^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 90 degrees

Review

55 + 120 + 95 + 90 = 360 degrees, a valid quadrilateral. And 90 + 90 = 180 degrees fills the straight line. The marked angle 90 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 90 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!
Variant 5 answer: 80 degrees

Find the measure of angle x.

40° 130° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 40 degrees, upper-left 130 degrees, and bottom-right 90 degrees (a right angle on the line). The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 40 degrees.
  • Upper-left inside angle = 130 degrees.
  • Bottom-right inside angle = 90 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−40∘−130∘−90∘=100∘360^\circ - 40^\circ - 130^\circ - 90^\circ = 100^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (100 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−100∘=80∘180^\circ - 100^\circ = 80^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 80 degrees

Review

40 + 130 + 90 + 100 = 360 degrees, a valid quadrilateral. And 100 + 80 = 180 degrees fills the straight line. The marked angle 80 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 80 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!
Variant 6 answer: 70 degrees

Find the measure of angle x.

65° 105° 80° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 65 degrees, upper-left 105 degrees, and bottom-right 80 degrees. The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 65 degrees.
  • Upper-left inside angle = 105 degrees.
  • Bottom-right inside angle = 80 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−65∘−105∘−80∘=110∘360^\circ - 65^\circ - 105^\circ - 80^\circ = 110^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (110 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−110∘=70∘180^\circ - 110^\circ = 70^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 70 degrees

Review

65 + 105 + 80 + 110 = 360 degrees, a valid quadrilateral. And 110 + 70 = 180 degrees fills the straight line. The marked angle 70 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 70 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!
Variant 7 answer: 70 degrees

Find the measure of angle x.

60° 100° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 60 degrees, upper-left 100 degrees, and bottom-right 90 degrees (a right angle on the line). The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 60 degrees.
  • Upper-left inside angle = 100 degrees.
  • Bottom-right inside angle = 90 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−60∘−100∘−90∘=110∘360^\circ - 60^\circ - 100^\circ - 90^\circ = 110^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (110 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−110∘=70∘180^\circ - 110^\circ = 70^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 70 degrees

Review

60 + 100 + 90 + 110 = 360 degrees, a valid quadrilateral. And 110 + 70 = 180 degrees fills the straight line. The marked angle 70 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 70 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!
Variant 8 answer: 70 degrees

Find the measure of angle x.

50° 110° x°
Show solution

Understand

A four-sided figure stands on a straight line. Three of its inside corners are known: top 50 degrees, upper-left 110 degrees, and bottom-right 90 degrees (a right angle on the line). The marked angle is the angle outside the bottom-left corner, between the figure's left side and the line.

Givens
  • The figure is a quadrilateral (4 corners), so its inside angles add to 360 degrees.
  • Top inside angle = 50 degrees.
  • Upper-left inside angle = 110 degrees.
  • Bottom-right inside angle = 90 degrees.
  • The marked angle and the bottom-left inside angle together lie along the straight line, so they add to 180 degrees.
Unknowns
  • The measure of the marked angle (between the left side and the line).
Constraints
  • All four inside angles of the quadrilateral total 360 degrees.
  • A straight angle is 180 degrees.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First subproblem: find the missing fourth inside angle using the 360-degree quadrilateral total. Second subproblem: the marked angle is what is left of the 180-degree straight angle after the inside corner, so subtract.

Execute

#7 Identify Subproblems 4.MD.C.7
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
360∘−50∘−110∘−90∘=110∘360^\circ - 50^\circ - 110^\circ - 90^\circ = 110^\circ
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
#7 Identify Subproblems 4.MD.C.7
At the bottom-left corner the inside angle (110 degrees) and the marked angle sit side by side along the straight line, so together they make 180 degrees. Subtract to get the marked angle.
180∘−110∘=70∘180^\circ - 110^\circ = 70^\circ
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
Answer: 70 degrees

Review

50 + 110 + 90 + 110 = 360 degrees, a valid quadrilateral. And 110 + 70 = 180 degrees fills the straight line. The marked angle 70 degrees is consistent.

Draw the diagram (tool 1) and check by measuring with a protractor that 70 degrees fits the wedge between the leaning side and the floor.

Standards · min grade 4

  • 4.MD.C.7 Recognize angle measure as additive and solve addition and subtraction problems — Adding and subtracting angle measures with the 360-degree and 180-degree totals.
  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
💡 Find the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!