Angle Facts in a Figure
Unknown angles fall out of a small set of facts: a straight line is 180 degrees, a triangle sums to 180, a quadrilateral to 360, angles combine and split, and parallel lines give equal corresponding/alternate angles. Learners apply these from clock faces and single figures up to polygon angle sums via triangulation and auxiliary lines. The method is choosing the right fact and chaining equations.
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Progression (13)
4-1 1. A clock face is twelve equal 30-degree parts 4.MD.C.64.MD.C.7
4-1 2. Small angles combine into larger angles 4.MD.C.74.MD.C.5
4-1 3. Use the 180-degree line to find figure angles 4.MD.C.7
4-1 4. Split a polygon into triangles to sum angles 4.MD.C.7
4-1 5. Quadrilateral angles sum to 360 degrees 4.MD.C.7
4-1 6. A straight line is 180 degrees 4.MD.C.7
4-1 7. Triangle angles sum to 180 degrees 4.MD.C.7
4-2 8. Draw an auxiliary parallel line to find a bent angle 4.G.A.1
4-2 9. Corresponding and alternate angles are equal 4.G.A.1
4-2 10. Adjacent angles of a parallelogram sum to 180 4.G.A.2
4-2 11. Perpendicular is half of a straight angle 4.G.A.14.MD.C.7
4-2 12. Exterior angle sum of a regular polygon is 360 4.G.A.24.MD.C.7
4-2 13. Polygon angle sum via triangulation from a vertex 4.G.A.2