Question

If each interior angle of a regular polygon is 120°, then it has ___ sides.

• A. 12
• B. 11
• C. 6
• D. 9

Answer 1

The correct option is C

6

Given that each interior angle of a regular polygon is 120°

For any polygon, interior angle + exterior angle = ${180}^{\circ }$

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

$\Rightarrow {120}^{\circ }+e={180}^{\circ }$

$\Rightarrow e={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

Number of sides of a polygon $\left(n\right)=\frac{{360}^{\circ }}{e}$

$\Rightarrow \left(n\right)=\frac{{360}^{\circ }}{{60}^{\circ }}$

$\Rightarrow \left(n\right)=6$