Central Angles and Intercepted Arcs - Problem 1
We can apply what we know about central angles and congruent chords in a circle to a problem like this. Well, we’re trying to find two different things, one the measure of angle B and two the measure of arc A.
Let’s start with the measure of arc A. if I look at A, it is the intercepted arc of this central angle, 155 degrees. So if I go back to what I know about a central and its intercepted arc, we said that they’re going to be equal to each other, which means A has to be equal to 155 degrees. Also this is the measure of arc A, is 155 degrees.
Second variable we’re solving for is B. If I look at B, it is the central angle that intersects a chord that is congruent to this central angle of 82 degrees, which means these two must be congruent something that we noticed when we said congruent chords have congruent central angles and congruent arcs, which means if B is congruent to 82, then B must be 82 degrees.
So the key here was remembering that chords have congruent, if the chords are congruent they have congruent central angle and that the central angle is congruent to its intercepted arc.