Question

Find the sum of the measures of the interior angles of a convex 10-gon.

Short answer

The sum of the measures of all interior angles of a convex 10-gon is $1440°$.

Step-by-step solution

Step 1. Given Information.

The polygon is convex 10-gon.

Step 2. Formula used.

The sum of the measure of the all-interior angles of a convex n-gon is $\left(n-2\right)\times 180°$.

Step 3. Calculation.

Here, polygon is convex heptagon this is $n=10$.

Calculate the sum of the all-interior angle of a convex 10-gon.

$\begin{array}{c}\left(n-2\right)\times 180°=\left(10-2\right)\times 180°\\ =8\times 180°\\ =1440°\end{array}$

Step 4. Conclusion.

The sum of the measures of all interior angles of a convex 10-gon is $1440°$ .