Question

The interior angles of a polygon are in A.P. The smallest angle is ${52}^{\circ }$ and the common difference is $8^{\circ }$. Find the number of sides of the polygon

• A. 3 or 30
• B. 5 or 50
• C. 2 or 20
• D. 4 or 40

Answer 1

The correct option is A

3 or 30

Here, $a={52}^{\circ }$ and $d=8^{\circ }$
Let the polygon have n sides. Then, the sume of interior angles of the polygon is
$(n-2){180}^{\circ }$
$S_n=(n-2)180$
$\frac{n}{2}[2a+(n-1\left)d\right]=(n-2)180$
$\frac{n}{2}[104+(n-1\left)8\right]=(n-2)180$
$\frac{n}{2}[8n+96]=(n-2)180$
$8n^2+96n=360n-720$
$(n-30)(n-3)=0$
$n=30$ or $3$