Question

The measure if an exterior angle of a regular polygon is given below find the measure of an interior angle then find the number of sides
24​

Answer 1

Answer:

The measure of the interior angle is 156°

The polygon has 15 sides

Step-by-step 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