Question

In circle O, RT and SU are diameters.

Circle O is shown. Line segments S U and R T are diameters. Line segment O V is a radius. Point V is between points R and U. Angle W O R is (13 x) degrees and angle T O U is (15 x minus 8) degrees.

If mArc R V = mArc V U , what is mArc V U ?

47°
52°
64°
87°

Answer 1

Interpret S = W (the diagram label), so angle SOR = 13x and angle TOU = 15x − 8.

Because SU and RT are diameters, OS and OU are opposite rays and OR and OT are opposite rays, so angle SOR = angle TOU. Thus
13x = 15x − 8 → 2x = 8 → x = 4.

Then angle SOR = 13·4 = 52°. Arc RU = 180° − 52° = 128° (central angle ROU), and since RV = VU, arc VU = 128°/2 = 64°.

Answer: 64°.