Pergunta
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
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PriscilaElite · Tutor por 8 anos
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To find the number of sides of a regular polygon given the measure of its exterior angle, we can use the formula:<br /><br />Number of sides = 360° / Exterior angle<br /><br />In this case, the exterior angle is given as 24°. Plugging this value into the formula, we get:<br /><br />Number of sides = 360° / 24° = 15<br /><br />Therefore, the polygon has 15 sides.<br /><br />To find the measure of each interior angle of a regular polygon, we can use the formula:<br /><br />Interior angle = (180° * (n - 2)) / n<br /><br />where n is the number of sides of the polygon.<br /><br />In this case, the number of sides is 15. Plugging this value into the formula, we get:<br /><br />Interior angle = (180° * (15 - 2)) / 15 = (180° * 13) / 15 = 2340° / 15 = 156°<br /><br />Therefore, the measure of each interior angle of the polygon is 156°.
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