Answer: m∠O = 64°
Step-by-step explanation:
The information was given: m∠R = 32°
O is the centre of the circumference and N, Q and R lies on it.
Also, the angle O is an angle at the centre because is the angle formed by the centre O with N and Q. The angle R is an angle at the circumference because R lies on the circunference's edge.
I'm used to say that when we have an angle in a circumference, it can "see" an arcle,part of a circumference. In this case, the angle R can "see" the arc NQ. The same is happening with the angle O, which can also "see" the arc NQ. When we have different angles "seeing" same arcles, there is a theorem who connect both angles.
The theorem says that angle at the centre is twice the angle at the circumference (Circle Theorem), so:
the angle at the centre (angle O) is twice the angle at the circumference (angle R)
m∠O = 2× m∠R
m∠O = 2 × 32°
m∠O = 64°
