what is the measure of < a

a) 37

b) 42

c) 55

d) 138

We know that an inscribed angle is half of the angle of the arc that it intercepts.

If you look closely, you’ll notice that angle B and angle D actually cover the entire circle.

Knowing this, we know that the sum of their angles in 180, since the sum of the angles of the arcs they intercept is 360.

Thus, we can form an equation:

3x - 5 + 2x = 180

Simplify:

5x - 5 = 180

Add 5 to both sides to isolate x:

5x = 185

Divide both sides by 5:

x = 37

Option A, or x = 37

-T.B.