If an exterior angle measure of a regular polygon is 24^circ how many sides does the polygon have? 12 16 18 None of the above What is the measure of each interior angle? square

Question

If an exterior angle measure of a regular polygon is 24^circ how many sides does the polygon have? 12 16 18 None of the above What is the measure of each interior angle? square

Answer 1

To find the number of sides of a regular polygon given the measure of its exterior angle, we can use the formula:Number of sides = 360° / Exterior angleIn this case, the exterior angle is given as 24°. Plugging this value into the formula, we get:Number of sides = 360° / 24° = 15Therefore, the polygon has 15 sides.To find the measure of each interior angle of a regular polygon, we can use the formula:Interior angle = (180° * (n - 2)) / nwhere n is the number of sides of the polygon.In this case, the number of sides is 15. Plugging this value into the formula, we get:Interior angle = (180° * (15 - 2)) / 15 = (180° * 13) / 15 = 2340° / 15 = 156°Therefore, the measure of each interior angle of the polygon is 156°.

Question

If an exterior angle measure of a regular polygon is 24^circ how many sides does the polygon have? 12 16 18 None of the above What is the measure of each interior angle? square

Solution

Resposta