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Given a regular pentagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon.

45°; 225°
40°; 220°
60°; 210°
72°; 54°

User Dunfield
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1 Answer

2 votes

Answer:

36°; 108°

Explanation:

The measure of each interior angle of a regular pentagon is 108°.a) Two consecutive radii are joined to form an angle. The sum of these two angles is equal to 360° as a full rotation. Therefore, each angle formed by two consecutive radii measures (360°/5)/2 = 36°.b) A radius and a side of the polygon form an isosceles triangle with two base angles of equal measure. The sum of the angles of this triangle is 180°. Therefore, the measure of the angle formed by a radius and a side is (180° - 108°)/2 = 36°. Thus, the angle formed by the radius and the side plus two consecutive radii angles equals 180°. Hence, the angle formed by a radius and a side measures (180° - 36° - 36°) = 108°.Therefore, the measures of the angles formed by two consecutive radii and a radius, and a side of the polygon are 36° and 108°, respectively. Thus, the answer is 36°; 108°.

User Xiomara
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