Question

The sum of all interior angle s of a regular polygon is 1080. What is the measure of each of its interior angles

Answer 1

The sum of all interior angles of an n sided regular polygon = (n - 2)180°.

$(n - 2)180 = 1080 \\ \\ n - 2 = \frac{1080}{180} = 6 \\ \\ n = 6 + 2 = 8$

It is a regular octagon, 8 sides it has.

Exterior angle = 360°/8 = 45°

Interior angle = 180° - 45° = 135°

135° is the answer.

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