Question

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of $\angle BAE$

• A. ${88}^{\circ }$
• B. ${108}^{\circ }$
• C. ${98}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is B ${108}^{\circ }$

In a regular pentagon ABCDE, BE is a diagonal.
$\angle BAE$ is the interior angle of the polygon.
Each interior angle of a regular polygon is = $\frac{{180}^o(n-2)}{n}$
where $n=$ number of sides of polygon, $n=5$
$\angle BAE=\frac{{180}^o(5-2)}{5}={108}^o$