WAEC 2019 · Paper 1 · Q32

Angles, triangles & polygons

The interior angles of a polygon are $3x^\circ$ , $2x^\circ$ , $4x^\circ$ , $3x^\circ$ and $6x^\circ$ . Find the size of the smallest angle of the polygon.

Worked solution (try it first)

There are five angles, so the polygon is a pentagon.
Its angles add up to $(5 - 2) \times 180^\circ = 540^\circ$ .
$3x + 2x + 4x + 3x + 6x = 540$ , so $18x = 540$ and $x = 30$ .
The smallest angle is $2x = 60^\circ$ , option B.

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