## kcla1996 2 years ago 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°

1. kcla1996

help???

2. Directrix

@kcla1996 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.

3. Directrix

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 = ?

4. Directrix

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.