Question

The correct formula(s) to find the measure of interior angle of a $n-$sided regular polygon is/are:

• A. $\frac{(n-2){180}^o}{n}$
• B. $\frac{(n-2){360}^o}{n}$
• C. ${180}^o-\frac{\text{Sum of exterior angles}}{n}$
• D. ${360}^o-\frac{\text{Sum of exterio angles}}{n}$

Answer 1

Answer: (A), (C)

${180}^o-\frac{\text{Sum of exterior angles}}{n}$

We know that sum of interior angles $=(n-2)\times {180}^o$
where $n$ is the total number of sides.

The polygon is regular. Hence, all the interior angles are of same measure.

$\therefore$ Measure of each angle

$=\frac{\text{Sum of interior angles}}{\text{Total number of sides}}$
$=\frac{(n-2)\times {180}^o}{n}$

$\therefore$ Option (a) is correct.

We know that sum of exterior angles of any polygon is ${360}^o.$
For regular polygon, the interior angles are same in measure and the exterior angles are also same in measure.

$\therefore$ Each exterior angle is $\frac{{360}^o}{n}$

Also, measure of interior angle
$={180}^o-\text{measure of exterior angle}$
$={180}^o-\frac{{360}^o}{n}$

Hence, option (c) is also correct.