Since the inscribed angle x^(∘) intercepts the arc that measures 44^(∘), we can say that x is half of 44.
x=1/2(44) ⇔ x=22
Therefore, x^(∘)=22^(∘).
Finding y
We can once again apply the Inscribed Angle Theorem.
In this case, the inscribed angle measures 54^(∘) and the measure of the arc is y^(∘).
54=1/2(y) ⇔ y=108
We have found that y^(∘)=108^(∘).
Finding w
Let's now find the value of w. Note that the angle of measure w^(∘) and the missing angle in the triangle are vertical angles. Therefore, their measures are equal.
To find the measure of the missing angle, recall the Triangle Angle Sum Theorem. The theorem states that the angle measures in a triangle add up to 180.
