Question

If each interior angle of a regular polygon measures ${140}^{\circ }$; the polygon has ___ sides.

• A. 12
• B. 13
• C. 14
• D. 16

Answer 1

The correct option is A

12

Let the regular polygon have n sides.

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

$\therefore e^{\circ }=180-{140}^{\circ }$

$e^{\circ }={40}^{\circ }$

We know $n=\frac{{360}^{\circ }}{e^{\circ }}$

$=\frac{{360}^{\circ }}{{40}^{\circ }}$

= 12