The exterior angles of a pentagon are in the ratio $2 : 1 : 4 : 3 : 5$ . Find each angle of the pentagon.

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Solution

sum of exterior angles $= 360$
$2 K + 1 K + 4 K + 3 K + 5 K = 30$
$15 K = 360$
$k = 24$
angles are $\begin{matrix} 2 K & k & 4 k & 3 k & 5 k ↓ & ↓ & ↓ & ↓ & ↓ 48 & 24 & 96 & 72 & 120 \end{matrix}$
subtract each from $180^{o}$ to get interior angle
$180 - 48 \Rightarrow 132$
$180 - 24 \Rightarrow 156$
$180 - 96 \Rightarrow 84$
$180 - 72 = 108$
$180 - 120 = 60$

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