Since the inscribed angle b^(∘) intercepts the arc that measures 140^(∘), we can say that b is half of 140.
b=1/2(140) ⇔ b=70
We have found that b^(∘)=70^(∘).
Finding c
To find the value of c, first recall that the measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. Therefore, the measure of the intercepted arc is twice the measure of the formed angle. In this case, the measure of the angle is equal to c^(∘), and the measure of the arc is 2 c^(∘)= 2c^(∘).
Let us first find the measure of the intercepted arc measuring 2c^(∘). A complete turn of a circle measures 360^(∘), and we know from the digram that this circle is broken into arcs measuring 125^(∘), 140^(∘), and 2c^(∘). We can use the Arc Addition Postulate to find the value of c.
