Question

In the given figure, $AED$ is an isosceles triangle with $AE=AD.ABCD$ is a parallelogram and $EGF$ is a line segment. If $\angle DCF={65}^{\circ }$ and $\angle EFB={100}^{\circ }$, then the number of diagonals of a regular polygon having its each exterior angle equal to the measure of $\angle AEG$, is

Answer 1

$\angle AED=\angle ADE=\angle GDE$

$\angle DCF=65°$

$⟹\angle ADE=65°$ (Corresponding angles are equal)

$\angle EFB=\angle FEC+\angle FCE$ (Sum of interior opposite angles is equal to the exterior angle)

$\angle FEC=35°$

Thus, $\angle AEG=65°-35°=30°$

We know, ext angle of a regular polygon having $n$ sides $=$ $\frac{360°}{n}$

$⟹n=12$