Question

In the given pentagon ABCDE, AB = BC = CD = DE = AE. What is the value of x?

• A. ${36}^{\circ }$
• B. ${54}^{\circ }$
• C. ${72}^{\circ }$
• D. ${108}^{\circ }$

Answer 1

The correct option is B ${54}^{\circ }$

Since, equal chords subtend equal angles at the centre.
$\therefore \angle AOE=\frac{{360}^{\circ }}{5}={72}^{\circ }$ (total angle subtended at the centre is ${360}^{\circ }$ and here it is subtended by 5 equal chords. We know that equal chords subtend equal angle at the centre)
Now, $OE=OA\Rightarrow \angle OEA=\angle OAE=x^{\circ }$
In $\Delta OAE,\angle x+\angle x+\angle AOE={180}^{\circ }$
$\Rightarrow 2x+{72}^{\circ }={180}^{\circ }$
$\Rightarrow x=\frac{{108}^{\circ }}{2}={54}^{\circ }$