Question

The figure below is the intersection of 3 line segments.

Answer 1

Answer: Choice A) 123 degrees

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Explanation:

Angle FOE is a straight angle as segment FE is a straight line, with point O on this line segment. Because FOE is a straight angle, we know that the three angles that make up angle FOE will combine to 180

(angle FOC)+(angle COB) + (angle BOE) = 180

Let x be the measure of angle COB. Plug in this and the other angle measures shown

(angle FOC)+(angle COB) + (angle BOE) = 180

(31)+(x)+(26) = 180

x+(31+26) = 180

x + 57 = 180

x+57-57 = 180-57

x = 123

Angle COB is 123 degrees.

Angle AOD is also 123 degrees because

angle COB = angle AOD

due to the fact these angles are vertical angles. Vertical angles are always congruent.