Exterior angles give the number of sides away
Using exterior angles to work out the number of sides of a regular polygon and its interior angle.
The Question
A regular polygon has an exterior angle of 24°. How many sides does it have, and what is the size of each interior angle?
The Answer
Reveal the Answer
Exterior angles always total 360°, so 360 ÷ 24 = 15 sides. Interior and exterior sit on a straight line, so 180 − 24 = 156°. Walking the perimeter and turning 24° each time makes the 360 obvious.
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Practice Sheet + Marked Answers
The four-question practice sheet, the solutions in our teaching voice and a self-marking quiz for this question are part of The Question Desk course — every school day of the term, with progress you can see. Enrolled group students get it included.
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