Question

If m arc ST = 96°, then m∠Q = ________.

m∠R
m∠S
m∠T
m∠W

Answer 1

The answer is m line segment R

Answer 2

m∠R

Explanation:

Q is the inscribed angle formed by the interception of segments TQ and SQ

R is the inscribed angle formed by the interception of segments TR and SR

The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle; then, both angles Q and R are half of the central angle and equal between them. Therefore, the angle does not change as its vertex is moved to different positions on the circle.