Since the inscribed angle a^(∘) intercepts the arc that measures 60^(∘), we can say that a is half of 60.
a=1/2(60) ⇔ a=30
We have found that a^(∘)=30^(∘).
Finding b
We can once again apply the Inscribed Angle Theorem.
The inscribed angle b^(∘) intercepts the arc that measures 84^(∘).
b=1/2(84) ⇔ b=42
We have found that b^(∘)=42^(∘).
Finding c
Look closely at the arc in which the angle of measure c^(∘) is inscribed.
By the Arc Addition Postulate, the arc's total measure is a sum of measures of the two arcs it consists of.
60+ 100= 160
Once again the Inscribed Angle Theorem applies. The inscribed angle which measures c^(∘) intercepts the arc that measures 160^(∘).
c=1/2(160) ⇔ c=80
Therefore, we know that c^(∘)=80^(∘).
Finding d
Note that the arcs of measures 100^(∘), 60^(∘), 84^(∘), and d^(∘) make a whole circle. Therefore, their measures must add up to 360^(∘). We will use this fact to find the measure of d.
