Question

In circle M shown, diameter SW intersects chord VT at R such that m arc VS = 146 degrees and m arc ST = 64 degrees. Which of the following is the measure of angle VRW

(1) 37

(2) 44

(3) 49

(4) 52

Please provide an explanation

Answer 1

(3) 49

Explanation:

The circle diagram is attached below. angle mVS = 146°

and angle mST = 64°.

mWT = 360 -64 - 146 = 150 (angle at a point)

∠ VWS = 73° = mVS / 2

MVW = 180 - 146 = 34 (angle in a straight line)

MVW = 180 -73 - 34 = 73° (angle in a triangle)

∠TMR = 180 - 64 = 116° (angle on a straight line)

∠VMT = 116 + 34 = 150°

∠ MVT = ∠ MTV (base angles of an isosceles triangle)

150 +2∠ mTV = 180

∠ MTV = 15°

∠RVW = 73 - 15 = 58°

∠RVW + ∠ VWS + ∠VRW = 180

∠VRW = 180 - 58 - 73 = 49