Question

ABCDE is a regular pentagon with sides of length $6$ cm. CD is also a side of a regular polygon with n sides. Given that $\angle EDF={90}^{\circ }$, find $n$.

• A. $18$
• B. $10$
• C. $20$
• D. $12$

Answer 1

Answer: (C)

$20$

ABCDE is a pentagon. Hence, $\angle EDC={108}^{\circ }$ (Interior angle of a pentagon)
Also, $\angle EDF={90}^{\circ }$
Now, $\angle CDF={360}^o-\angle EDF-\angle EDC$
$\angle CDF={360}^o-{90}^o-{108}^o={162}^o$
Now, Interior angle of a polygon,
$\frac{{180}^o(n-2)}{n}={162}^o$
$180n-360=162n$
$18n=360$
$n=20$
Thus, polygon has $20$ sides.