Question

If m∠R = 28 , find m∠O. The figure is not drawn to scale. Help please

Answer 1

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.

Answer 2

56 degrees.

I've done this quiz before and I missed that exact question - the correct answer was 56.