Question

If the sum of all the angles of a polygon except one angle is ${2220}^{\circ }$, then the number of sides of the polygon are:

• A. 12
• B. 13
• C. 14
• D. 15

Answer 1

Answer: (D)

15

Sum of angles of polygon with $n$ sides $=(n-2)\times {180}^{\circ }\dots \left(1\right)$

The sum of the angles of a polygon should be a multiple of ${180}^{\circ }$.

But, ${2220}^{\circ }={180}^{\circ }\times 12+{60}^{\circ }$

${2220}^{\circ }$ + ${120}^{\circ }$ = ${2340}^{\circ }$

$(x-2)=\frac{2340}{180}\dots$ (From $\left(1\right)$)

$x-2=13$

$\Rightarrow x=15$
Therefore, the number of sides of the polygon is $15$.