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geometry

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In a polygon, 6 of the interior angles are right angles and each of the remaining interior angles is 200 degrees. What is the number of sides of the polygon?

Jul 8, 2020

#1
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In a polygon, 6 of the interior angles are right angles and each of the remaining interior angles is 200 degrees.
What is the number of sides of the polygon?

$$\text{Let the number of sides of the polygon = n }$$

$$\begin{array}{|rcll|} \hline \mathbf{6*90^\circ + (n-6)*200^\circ} &=& \mathbf{(n-2)*180^\circ} \\ 540^\circ + 200^\circ n-6 *200^\circ &=& 180^\circ n-2 *180^\circ \\ 200^\circ n-660^\circ &=& 180^\circ n-360^\circ \\ 20^\circ n &=& 300^\circ \quad | \quad : 20^\circ \\ n &=& \dfrac{300^\circ } {20^\circ} \\\\ \mathbf{ n } &=& \mathbf{15} \\ \hline \end{array}$$

Jul 8, 2020