Question

Each interior angle of a regular polygon is 144°. The measure of each interior angle of a regular polygon which has double the number of sides as the first polygon is

• A. ${150}^{\circ }$
• B. ${152}^{\circ }$
• C. ${160}^{\circ }$
• D. ${162}^{\circ }$

Answer 1

The correct option is D

${162}^{\circ }$

Solution: Exterior angle (e) = ${180}^{\circ }$ - interior angle ……. (Polygon is regular)
e = ${180}^{\circ }-{144}^{\circ }$
e = ${36}^{\circ }$
Number of sides (n) = $\frac{{360}^{\circ }}{\text{Exterior angle}}$
Number of sides (n) = $\frac{{360}^{\circ }}{{36}^{\circ }}$
= 10
The number of sides of the new polygon = 2n = 20
Exterior angle (e) = $\frac{{360}^{\circ }}{\text{number of sides}}$
= $\frac{{360}^{\circ }}{20}$
= 18°
Interior Angle = ${180}^{\circ }$- Exterior Angle
= ${180}^{\circ }-{18}^{\circ }$
= ${162}^{\circ }$
Hence (D)