Question

In circle O, m∠R = 23. Find m∠O. (The figure is not drawn to scale.)

Answer 1

Angle R is an inscribed angle. By the inscribed angle theorem, angle O (which is a central angle corresponding to the same arc as angle R) will be double that of angle R.

So in short,

(central angle O) = 2*(inscribed angle R)
(central angle O) = 2*(23)
(central angle O) = 46 degrees

The final answer is 46 degrees