Question

Find the unknown angle $x$ in the above figure.

• A. ${60}^0$
• B. ${90}^0$
• C. ${108}^0$
• D. ${120}^0$

Answer 1

The correct option is C ${108}^0$

The given figure is a regular pentagon since it has $5$ sides and all are equal

We know that the sum of the internal angles $S_n$ of an $n$ sided convex polygon is $(n-2)\times {180}^o$

Here $n=5,$ i.e $S_n=(5-2)\times {180}^o={540}^o.......\left(i\right)$

In a regular polygon, all the sides are equal and all the angles are equal to each other

$\therefore 5x={540}^o$

$\Rightarrow x={108}^o$