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In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper. If x+y = $80^{\circ}$ . How many sides does the polygon have?

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Ten

Nine

Eight

Seven

answer is B.

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Detailed Solution

The two angles that aren’t part of the polygon add up to

80^{\circ}

, and a quadrilateral’s angles add up to

360^{\circ}

, it can be said that the angles of the polygon add up to

280^{\circ}

, and therefore each angle in the polygon is

140^{\circ}

\frac{(n - 2) 180^{\circ}}{n} = 140^{\circ}

\Rightarrow 180^{\circ} n - 360^{\circ} = 140^{\circ} n

\Rightarrow 40^{\circ} n = 360^{\circ}

\Rightarrow n = 9

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