Given a regular octagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon.
A. 72°; 252°
B. 36°; 216°
C. 45°; 67.5°
D. 40°; 230°
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Circles can be circumscribed about and inscribed regular polygons. Hence, some of the terminology associated with circles turns up in the study of regular polygons.
The radius of a regular octagon is the radiusof the circle that can be circumscribed about it.
On the attached figure above, you see <1 as an angle formed by consecutive radii. A complete circle rotations is 360 degrees and there are 8 central angles, all congruent. So angle 1 has measure 360/8 = ?
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Once you get the measure of angle 1, then the angle formed by a radius and a side of the octagon is one of the two base angles of the isosceles triangle of which angle 1 is the vertex angle. Recall that the sum of the angle measures of a triangle is 180 and that base angles of an isosceles triangle are congruent and you will have the angle for part b.