Question

In circle O, mR = 23. Find mO. (The figure is not drawn to scale.)

67

157

46

23

Answer 1

m∠O = 46°.

For inscribed angles, the measure of the inscribed angle is equal to half of the measure of the intercepted arc.  This means that m∠R = 1/2(NQ);
23 = 1/2(NQ)

Multiply both sides by 2:
46 = NQ

The measure of the central angle is equal to the measure of the intercepted arc; m∠O = NQ; m∠O = 46