Polygons and Geometrical Constructions

Given z = 114 deg

You are asked to construct a triangle of sides 1 cm, 3 cm and 5 cm. Explain if you are able to do so.

Find the sum of the interior angles of a polygon with 11 sides.

Answer explanation

Note: Sum of interior angles = (n-2) × 180° = (11-2) × 180° = 9 × 180° = 1620°

What is the size of each interior angle of a regular octagon?

Answer explanation

Note: Sum of interior angles = (n-2) × 180° = (8-2) × 180° = 6 × 180° = 1080°

Each interior angle = 1080° / 8 = 135°

Method 2:

Sum of exterior angles = 360°

Each exterior angle = 360° / 8 = 45°

Each interior angle = 180° - 45° = 135°