Question

What is the sum of all interior angles of the polygon having $n$ number of sides.

• A. ${360}^o(n-2)$
• B. ${180}^o(n-2)$
• C. ${180}^o(n-1)$
• D. ${360}^o(n-1)$

Answer 1

The correct option is B ${180}^o(n-2)$

The sum of all angles of polygon is given by ${180}^o(n-2)$. where $n$ is the number of sides.

According to formula: sum of all interior angles of a triangle is $(3-2)\times {180}^o={180}^o$ because a triangle has 3 sides.


Lets us see for polygon having $4$ sides,
Sum of all interior angles of a polygon with 4 sides is $(4-2)\times {180}^o={360}^o$


Lets us see for polygon having $5$ sides,
Sum of all interior angles of a polygon with 5 sides is $(5-2)\times {180}^o={540}^o$

Hence, we can say that sum of all interior angles of any polygon having $n$ sides is given by ${180}^o(n-2)$.

Option $\left(b\right)$ correct.