Question

What is the measure of arc qr?

Answer 1

Answer-

The measure of arc QR is 104°

Solution-

The Central Angle Theorem-

It states that the measure of inscribed angle is always half the measure of the central angle.

Inscribed angle is the angle formed in the interior of a circle when two secant lines intersect on the circle.

A central angle is the angle that forms when two radii meet at the center of a circle.

Here,

∠QTR = Central angle

∠QSR = Inscribed angle = 52°

Applying the theorem,

m∠QTR = 2×m∠QSR = 2×52°=104°

Answer 2

Angle QSR is an inscribed angle and is equal to half the intercepted arc.
So if angle QSR = 52 degrees then the arc measures 104 degrees.
Source: http://www.1728.org/circangl.htm
(Look at the first graphic).