Question

Each interior angle of a regular polygon is ${144}^{\circ }$. Then 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

${162}^{\circ }$

Exterior angle (e)
$={180}^{\circ }-interiorangle$ ……. (Polygon is regular)
$e={180}^{\circ }-{144}^{\circ }$
$e={36}^{\circ }$

Number of sides (n)
$=\frac{{360}^{\circ }}{ExteriorAngle}$

$=\frac{{360}^{\circ }}{{36}^{\circ }}={10}^{\circ }$

The number of sides of the new polygon = 2n = 20
Exterior angle (e)
$=\frac{{360}^{\circ }}{numberofsides}$
$=\frac{{360}^{\circ }}{20}={18}^{\circ }$

Interior Angle
$={180}^{\circ }-ExteriorAngle$
$={180}^{\circ }-{18}^{\circ }$
$={162}^{\circ }$