Question

if the sum of the interior Angele measures of a convex ploygon is 2.60 how many sides does the polygon have?

Answer 1

The polygon has 14 sides.

Step-by-step explanation:

Given that the sum of the interior angles of the polygon is 2,160.

`T=2,160`

Recall that the sum of interior angles of a polygon can be calculated using the formula;

`\begin{gathered} T=180(n-2) \\ \text{where;} \\ n=\text{ number of sides} \\ T=\text{ sum of the interior angles of the polygon.} \end{gathered}`

Substituting the value of T, to solve for n;

`\begin{gathered} 2,160=180(n-2) \\ (2160)/(180)=n-2 \\ 12=n-2 \\ n=12+2 \\ n=14 \end{gathered}`

Therefore, the polygon has 14 sides.