Question

What is the sum of angles of a convex polygon whose number of sides is $10$?

Answer 1

Hint- In this question number of sides of convex polygon is given so that, in order to find the sum of angles, we must further subtract $2$ from the number of sides by multiplying it by $${180}^0$$ we will get the answer needed.

Complete step-by-step answer:
Given that the number of convex polygon sides is $10$
As we know the sum of the inner angles of a regular convex polygon ${}^{\prime }{n}^{\prime }$ sided is given by the formula:

$(n-2)\times {180}^0$

Where ${}^{\prime }{n}^{\prime }$ is the number of convex polygons on each side

Here the question is given as $10$

$n=10$.

Now, we are going to substitute the value of n in the formula above, so we have

$$\begin{gathered} =(10-2)\times {180}^0 \\ =8\times {180}^0 \\ ={1440}^0 \end{gathered}$$

Hence, the sum of angles of a convex polygon is $${1440}^0$$

Note- A regular polygon is a flat shape, all of whose sides are equal, and all of whose angles are equal. The formula to find the sum of the interior angle calculation is $(n-2)\times {180}^0$. We take the formula and divide it by the number of sides $(n-2)\times {180}^0÷n$. to find the value of one interior angle