The sum of the interior angle measures of a convex polygon is . How many sides does it have?
Number of sides

Ask by Carrillo Donnelly. in the United States

Mar 25,2025

Question

The sum of the interior angle measures of a convex polygon is $$ 1080^{\circ} $$. How many sides does it have? Number of sides $$ =\square $$

UpStudy AI · Accepted Answer

Let $$ n $$ be the number of sides of the polygon. The sum of the interior angles of a convex polygon is given by

$$
(n-2) \times 180^\circ
$$

Given that the sum is $$ 1080^\circ $$, we have

$$
(n-2) \times 180^\circ = 1080^\circ
$$

Dividing both sides by $$ 180^\circ $$,

$$
n-2 = \frac{1080}{180} = 6
$$

Adding 2 to both sides gives

$$
n = 6 + 2 = 8
$$

Thus, the number of sides is $$ \boxed{8} $$.
The polygon has 8 sides.

The sum of the interior angle measures of a convex polygon is . How many sides does it have?
Number of sides