Question

If a $\lambda$ polygon has 18 sides, then $\lambda$ each interior angle measures

• A. ${20}^{\circ }$
• B. ${120}^{\circ }$
• C. ${150}^{\circ }$
• D. ${160}^{\circ }$

Answer 1

The correct option is D

${160}^{\circ }$

In a regular polygon all its interior angles are equal and all its exterior angles are equal.
n = 18 (given)
exterior angle (e) $=\frac{{360}^{\circ }}{n}=\frac{{360}^{\circ }}{18}={20}^{\circ }\text{we know, interior angle}\left(i^{\circ }\right)+\text{exterior angle}\left(e^{\circ }\right)={180}^{\circ }{i}^{\circ }+{20}^{\circ }={180}^{\circ }\therefore i^{\circ }={160}^{\circ }$