WAEC 2021 · Paper 1 · Q15

Angles, triangles & polygons

The sum of the interior angles of a regular polygon with $k$ sides is $(3k - 10)$ right angles. Find the size of each exterior angle.

Worked solution (try it first)

A right angle is $90^\circ$ , and the angle sum is $(k - 2) \times 180^\circ$ .
So $(k - 2) \times 180 = (3k - 10) \times 90$ .
Divide by 90: $2k - 4 = 3k - 10$ , so $k = 6$ .
Each exterior angle is $360^\circ \div 6 = 60^\circ$ , option A.

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