UK EDITION

Interior and Exterior Angles of Regular Polygons

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The following formulae for regular polygons should be known:

Exterior angle = 360º ÷ no. of sides

Interior angle = 180º - exterior angle

Sum of interior angles = 180 x (no. of sides - 2)

**Example**

A regular polygon has an interior angle of 165.6º.

How many sides does it have?

**Answer**

Exterior angle = 180 - interior angle = 180 - 165.6 = 14.4º

No. of sides = 360 ÷ exterior angle = 360 ÷ 14.4 = **25**

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