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

Ask by Harrington Donnelly. in the United States

Mar 25,2025

Question

The sum of the interior angle measures of a convex polygon is $$ 1260^{\circ} $$. How many sides does it have? Number of sides $$ =\square $$

UpStudy AI · Accepted Answer

We start with the formula for the sum of the interior angles of a convex polygon with $$ n $$ sides:
$$
\text{Sum} = (n-2) \times 180^\circ.
$$

Since the sum is given as $$ 1260^\circ $$, we set up the equation:
$$
(n-2) \times 180^\circ = 1260^\circ.
$$

**Step 1: Divide both sides by $$ 180^\circ $$**
$$
n - 2 = \frac{1260}{180}.
$$

**Step 2: Simplify the fraction**
$$
n - 2 = 7.
$$

**Step 3: Solve for $$ n $$**
$$
n = 7 + 2 = 9.
$$

Thus, the number of sides is $$ \boxed{9} $$.
The polygon has 9 sides.

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