waecmaths question:
Three exterior angles of a polygon are 30o, 40o and 60o . If the remaining exterior angles are 46o each. Name the polygon.
Option A:
Decagon
Option B:
Nonagon
Option C:
Octagon
Option D:
Hexagon
waecmaths solution:
$\begin{align} & \text{Total sum of exterior angles in any polygon is 36}{{\text{0}}^{\circ }} \\ & {{30}^{\circ }}+{{40}^{\circ }}+{{60}^{\circ }}+n({{46}^{\circ }})={{360}^{\circ }} \\ & {{130}^{\circ }}+{{46}^{\circ }}(n)={{360}^{\circ }} \\ & {{46}^{\circ }}(n)={{230}^{\circ }} \\ & n=\frac{{{230}^{\circ }}}{{{46}^{\circ }}}=5 \\ & \text{The number sides the polygon is }3+5=8 \\ & \text{The polygon is an OCTAGON} \\\end{align}$
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