Question

if the sum of the measures of the interior angles of a polygon is twice the sum of its exterior angles, how many sides does it have?

Answer 1

6

Explanation:

The sum of the exterior angles of any polygon = 360°

Thus the sum of the interior angles = 2 × 360° = 720°

The sum of the interior angles of a polygon = 180° (n - 2), hence

180(n - 2) = 720 ← divide both sides by 180

n - 2 = 4 ← add 2 to both sides

n = 6

The polygon has 6 sides