Using one of the circle theorems, we have proven that the measure of ∠RTW is 15°
Circle Geometry
From the question, we are to complete the proof
From the given information,
[tex]m\overset{\huge\frown}{ST} = 30 ^\circ[/tex]
∴ m ∠SRT = 30°
Now, by one of the circle theorems, we have that
Angle at the center is twice the angle at the circumference
∴ ∠RWT = 30°/2
∠RWT = 15°
Consider ΔRTW
/RT/ and /RW/ are radii
Therefore, ΔRTW is an isosceles triangle
Then,
m ∠RWT = m ∠TRW (Base angles of an isosceles triangle)
∴ m ∠RTW = 15°
Hence, the measure of ∠RTW is 15° as proven above
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