Answer:
The measure of the interior angle is 156°
The polygon has 15 sides
Explanation:
Let us revise some facts in a polygon
- The sum of the exterior angles of any polygon is 360°
- At each vertex of a polygon, the exterior and interior angles formed a pair of linear angles (The sum of their measures is 180°)
- A regular polygon has equal angles and equal sides
In our question
∵ The measure of an exterior angle of a regular polygon = 24°
∵ The sum of measures of the interior angle and exterior angle at
a vertex of a polygon is 180°
∴ The measure of the interior angle = 180° - 24°
∴ The measure of the interior angle = 156°
∵ The sum of the exterior angles of any polygon is 360°
∵ The polygon is regular (all angles are equal in measures)
∴ The measure of each exterior angle = 360° ÷ n, where n the
number of its angles or sides
∴ 24° = 360°/n
→ Multiply both sides by n
∴ 24n = 360
→ Divide both sides by 24
∴ n = 15
∴ The polygon has 15 sides