TOPIC 8 · GRADES 3–4 STRETCH LEARNING

Angle Sums Inside Shapes

Discover why triangle angles total 180° and how diagonals reveal sums for larger polygons.

Enrichment beyond required Grade 3–4 benchmarks

BIG IDEA

A polygon with n sides can be split from one vertex into n − 2 triangles, so its interior-angle sum is (n − 2) × 180°.

WHAT TO KNOW

Every triangle's interior angles add to 180°.
A quadrilateral splits into two triangles, so its angles add to 360°.
A pentagon splits into three triangles (540°); a hexagon splits into four (720°).

WATCH OUT

The sum depends on the number of sides, not whether the polygon looks regular or tilted.

TRY IT

Change the polygon and count the triangle regions before checking the total.

Choose the next topic from the lesson rail when you are ready.