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!
+26367 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
\(\begin{array}{|rcll|} \hline \angle DEA &=& \dfrac{(5-2)*180^\circ}{5} \\ \angle DEA &=& \dfrac{3*180^\circ}{5} \\ \angle DEA &=& 3*36^\circ \\ \mathbf{\angle DEA} &=& \mathbf{108^\circ} \\\\ \angle AEF &=& \dfrac{(6-2)*180^\circ}{6} \\ \angle AEF &=& \dfrac{4*180^\circ}{6} \\ \angle AEF &=& 4*30^\circ \\ \mathbf{\angle AEF} &=& \mathbf{120^\circ} \\\\ \angle DEF &=& 360^\circ - \angle DEA - \angle AEF \\ \angle DEF &=& 360^\circ - 108^\circ - 120^\circ \\ \angle DEF &=& 360^\circ - 108^\circ - 120^\circ \\ \angle DEF &=& 360^\circ - 228^\circ \\ \mathbf{\angle DEF} &=& \mathbf{132^\circ} \\ \hline \end{array}\)
