Answer: The correct option is (D) 56°.
Step-by-step explanation: In the given figure, we have
m∠R = 28°.
We are to find the measure of ∠O.
In the attached figure, we have taken another point 'P' on the circumference of the circle.
In a circle, the angles subtended on the circumference by the same arc have equal measures.
In the attached figure, ∠P and ∠R are angles on the circumference of the circle subtended by the arc QN.
So, we have
m∠P = m∠R = 28°.
Also, an angle subtended by an arc at the center is twice the angle subtended by the same arc on the circumference of the circle.
Since ∠O is the angle subtended by the arc QN at the center and ∠P is the angle subtended by the same arc QN on the circumference, so we must have
m∠O = 2 × m∠P = 2 × 28° = 56°.
Thus, the measure of ∠O is 56°.
Option (D) is correct.
