Question

How do I find out these arc measures?

Answer 1

Angle SUR and PUQ are vertical angles and both = 42°

Line QS is a diameter and so angle PUQ + PTU + TUS = 180°

42° + 64° + angle TUS = 180° Therfore, angle TUS = 74°

Angle QUR + SUR = 180°. Therefore, angle QUR = 138°