Connect triangle totals to interior angles and one complete exterior turn.
This is the first lesson in its subject. A free account reads it in full.
You are reading the opening. Members read every lesson and guide in full. A free account reads the first lesson in each subject in full.
You are reading the opening. Your free account reads the first lesson in each subject in full. Members read every lesson and guide in full.
First lesson in this subject: Complete the angle sum
We couldn’t check your membership. Please reload and try again.
Members read every lesson and guide in full and practice without limits. View membership
Draw diagonals from one vertex of a convex polygon with n sides. The polygon splits into n − 2 triangles, so its interior angles total (n − 2) × 180°.
A pentagon splits into 3 triangles and has an interior-angle sum of 540°. This total does not require equal sides or equal angles. Divide it equally among the corners only when their angles are known to be equal, as in a regular polygon.
You are reading the opening. Members read every lesson and guide in full. A free account reads the first lesson in each subject in full.
You are reading the opening. Your free account reads the first lesson in each subject in full. Members read every lesson and guide in full.
First lesson in this subject: Complete the angle sum
We couldn’t check your membership. Please reload and try again.
Practice · Reason about interior angles, exterior turns and diagonals. Explore what regularity allows you to conclude.
Book · Explore measurements, transformations, coordinates and geometric relationships through diagrams and worked examples.
Previous lesson · Separate distance from midpoint by using differences for length and averages for location.
Next lesson · Use the central angle to take the same fraction of circumference or circle area.
Browser storage is unavailable. Changes last only on this page.