Exercise 15 Page 815

Since the inscribed angle — which measures 20^(∘) — intercepts the arc that measures a^(∘), we can say that 20 is half of a.

20=a/2 ⇔ a=40

The value of a is 40.

Finding b

Let's pay close attention to the arcs whose measures are a^(∘) and b^(∘).

An arc whose endpoints are the endpoints of a diameter is a semicircle and it has a measure of 180^(∘). Therefore, by the Arc Addition Postulate, the sum of a and b is equal to 180. Substituting a with 40 that we found, we can find the value of b.

b+ 40=180 ⇔ b=140

Thus, the value of b is 140.

Finding c

It is given that l is a tangent.

Recalling that a tangent is perpendicular to the radius at the point of tangency, we can find that the value of c as 90.