Question

The figure shows 3 regular pentagons put together. The measure of $\angle ABC$ is

• A. ${36}^{\circ }$
• B. ${63}^{\circ }$
• C. ${72}^{\circ }$
• D. ${27}^{\circ }$

Answer 1

The correct option is A

${36}^{\circ }$

For regular pentagon, n=5.

$\Rightarrow$ Each exterior angle $=\frac{360}{5}={72}^{\circ }$

$={72}^{\circ }$

Now, $e+i={360}^{\circ }$ (Linear pair)

$72+i={180}^{\circ }$

$\Rightarrow i={108}^{\circ }$

Now, ${108}^{\circ }+{108}^{\circ }+{108}^{\circ }+\angle ABC={360}^{\circ }$

$\Rightarrow {324}^{\circ }+\angle ABC={360}^{\circ }$

$\Rightarrow \angle ABC={360}^{\circ }-{324}^{\circ }$

$={36}^{\circ }$