Use the 180-degree line to find figure angles
4.MD.C.74.G.A.1
Generated variants — 8
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
Find the measure of angle x.
Show solution
1 · Understandwhat's really being asked
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.
2 · Planchoose the strategy
#7 Identify Subproblems
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.
3 · Execute2 carry out the plan
1Find the bottom-left inside angle
2Use the straight line at the bottom-left corner
4 · Reviewdoes it hold up?
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.
Standardsmin grade 4
4.MD.C.7Recognize 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.1Draw points, lines, line segments, rays, angles, and identify in figures — Reading the quadrilateral, its corners, and the line in the figure.
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