Question

The number of degrees in each angle of a regular decagon is

• A. ${120}^o$
• B. ${60}^o$
• C. ${180}^o$
• D. ${144}^o$

Answer 1

The correct option is D ${144}^o$

$\Rightarrow$ We know that decagon has 10 sides.

$\Rightarrow$ So, $n$ = 10

$\Rightarrow$ Sum of all interior angles of decagon = $(n-2)\times {180}^{\circ }$

So, each interior angle of decagon = $\frac{(n-2)\times {180}^{\circ }}{n}$

$\Rightarrow$ $\frac{(10-2)\times {180}^{\circ }}{10}$

$\Rightarrow$ $\frac{8\times {180}^{\circ }}{10}$ = ${144}^{\circ }$

$\therefore$ Each angle of regular decagon is ${144}^{\circ }$