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Regular pentagon ABCDE and regular hexagon AEFGHI are drawn on opposite sides of line segment AE such that they are coplanar. What is the degree measure of exterior angle DEF?

Here is the picture

Thank you in advance! 

 May 28, 2020
 #1
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Regular pentagon ABCDE and regular hexagon AEFGHI are drawn on opposite sides of line segment AE such that they are coplanar.

What is the degree measure of exterior angle DEF?

Here is the picture

 

\(\begin{array}{|rcll|} \hline \angle DEA &=& \dfrac{(5-2)*180^\circ}{5} \\ \angle DEA &=& \dfrac{3*180^\circ}{5} \\ \angle DEA &=& 3*36^\circ \\ \mathbf{\angle DEA} &=& \mathbf{108^\circ} \\\\ \angle AEF &=& \dfrac{(6-2)*180^\circ}{6} \\ \angle AEF &=& \dfrac{4*180^\circ}{6} \\ \angle AEF &=& 4*30^\circ \\ \mathbf{\angle AEF} &=& \mathbf{120^\circ} \\\\ \angle DEF &=& 360^\circ - \angle DEA - \angle AEF \\ \angle DEF &=& 360^\circ - 108^\circ - 120^\circ \\ \angle DEF &=& 360^\circ - 108^\circ - 120^\circ \\ \angle DEF &=& 360^\circ - 228^\circ \\ \mathbf{\angle DEF} &=& \mathbf{132^\circ} \\ \hline \end{array}\)

 

laugh

 May 28, 2020
 #2
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:o wow that helped a lot! I did not think that they would be coplanar...

Thanks!!

Guest May 28, 2020

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