Angles in polygons · Grade 10

In Grade 10 you learn: polygon problems with algebra.

A polygon’s interior angles always add up to the same total for a given number of sides, and its exterior angles always add up to 360°. For regular polygons this lets you find every angle, or the number of sides from one angle.

Key facts

  • Sum of interior angles = (n − 2) × 180°, for n sides.
  • The exterior angles of any polygon add up to 360°.
  • Interior angle + exterior angle = 180° at each corner.
  • Regular polygon: each exterior angle = 360° ÷ n.
  • Number of sides of a regular polygon = 360° ÷ exterior angle.

Worked examples

Example 1

Find each interior angle of a regular octagon.

Answer: 135°

Example 2

Each interior angle of a regular polygon is 156°. How many sides does it have?

Answer: 15

Other years