Question

If each interior angle of a regular polygon is ${170}^{\circ }$, then the polygon has ___ sides.

• A. 10
• B. 36
• C. 72
• D. 20

Answer 1

The correct option is B

36

Let the exterior angle of the given polygon be 'e'.

$\because$ exterior angle + interior angle = 180${}^{\circ }$

$\Rightarrow e+{170}^{\circ }={180}^{\circ }$

$\Rightarrow e={180}^{\circ }-{170}^{\circ }$

$e={10}^{\circ }$

$\because$ Sum of exterior angles in a polygon = 360${}^{\circ }$

$\Rightarrow$ n $\times$ e = 360${}^{\circ }$ (where, n is the number of sides in the polygon)

$\Rightarrow n=\frac{{360}^{\circ }}{e^{\circ }}$

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

= 36

$\therefore$ Number of sides = 36.