"The sum of the measures of the interior..." was answered by our community

Tiffany Page

Answered question

2022-11-06

The sum of the measures of the interior angles of a convex polygon is 540. How do you classify the polygon by the number of sides?

Paskcreessy4k5

Beginner2022-11-07Added 20 answers

Step 1
If n are number of sides of a convex polygon, sum of its interior angles is

(n - 2) \times 180^{\circ}

As in given case sum of interior angles is

540^{\circ}

, we have

(n - 2) \times 180^{\circ} = 540^{\circ}

n - 2 = \frac{540}{180} = 3

and

n = 3 + 2 = 5

Hence, polygon is a pentagon.

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