Question

The sum of the measure of the interior angles of a convex polygon is 2700º. Classify the polygon by the number of sides.choose your answer...

Answer 1

Step 1

Write equation for sum of interior angles of any polygon

`\begin{gathered} \text{Sum of interior angles of any polygon = (n - 2)180} \\ n\text{ = number of sides} \\ \text{Therefore,} \\ 2700\text{ = (n - 2)180} \\ \text{Divide through by 180} \\ \\ (2700)/(180)\text{ = }\frac{(n\text{ - 2)180}}{180} \\ n\text{ - 2 = 15} \\ n\text{ = 15 + 2} \\ n\text{ = 17} \end{gathered}`

Number of sides = 17