Question

Find the number of sides in a polygon, if the sum of its interior angles is ${1440}^{\circ }$.

• A. 10
• B. 8
• C. 15
• D. 6

Answer 1

The correct option is A 10

The sum of interior angles of polygon = ${1440}^{\circ }$

Let the number of sides = n

The sum of an interior angle of a polygon is (2n – 4) × ${90}^{\circ }$

The side of a polygon can be calculated as,

(2n – 4) × ${90}^{\circ }$ = ${1440}^{\circ }$

2n – 4 = $\frac{{1440}^{\circ }}{{90}^{\circ }}$

2(n – 2) = $\frac{{1440}^{\circ }}{{90}^{\circ }}$

n – 2 = $\frac{{1440}^{\circ }}{2\times {90}^{\circ }}$

We get,
n – 2 = 8
n = 8 + 2
n = 10
Hence, the number of sides in the polygon = 10