How much is an angle of a 36-sided regular polygon?

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Solution

Total number of sides of the given regular polygon = 36

We know that the sum of the angles of a polygon with n sides = (n −2) × 180°

Sum of the angles of the given regular polygon = (36 − 2) × 180°

= 34 × 180°

= 6120°

Let the measure of each angle of the given regular polygon be x°.

⇒ 36x = 6120°

⇒ x = 170°

Thus, the measure of each angle of the given regular polygon is 170°.

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