Recall that the measure of an arc is equal to the measure of its corresponding central angle. Therefore, the measure of the arc corresponding to the central angle with a^(∘) is equal to a^(∘).
Since the inscribed angle — which measures 45^(∘) — intercepts the arc that measures a^(∘), we can say that 45 is half of a.
45=a/2 ⇔ a=90
Thus, the value of a is 90.
Finding b
By the Inscribed Angle Theorem, we can find the value of b.
Since the inscribed angle — which measures 45^(∘) — intercepts the arc that measures b^(∘), we can say that 45 is half of b.
45=b/2 ⇔ b=90
Thus, the value of b is 90.
Finding c
The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
In our diagram, the angle whose measure is c^(∘) is formed by a tangent and a chord. Its intercepted arc has a measure of 140^(∘). Therefore, we know that c is half of 140.
c=140/2 ⇔ c=70
Thus, the value of c is 70.
Finding d
The tangent line to the given circle is a straight line.
