Answer: A) 76 degrees
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Explanation:
Angle PQT = 35 degrees is given. This inscribed angle subtends or cuts off minor arc PT. This is the shortest distance along the circle from P to T. Any other inscribed angle that cuts off this same arc will also be the same measure. Note how angle PRT is such an inscribed angle, so,
angle PRT = 35 degrees
which we'll use later.
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Focus on triangle ROS. Interior angle O is 180-82 = 98 degrees due to it being supplementary to the 82 degree angle shown.
Triangle ROS is isosceles with OR = OS being the two equal radii. The opposite base angles R and S are congruent angles. Call them x for now
(angle O) + (angle R) + (angle S) = 180
98+x+x = 180
2x+98 = 180
2x = 180-98
2x = 82
x = 82/2
x = 41
For triangle ROS, interior angle R is 41 degrees. Put another way,
angle ORS = 41 degrees
we'll use it below along with angle PRT
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angle PRS = (angle PRT) + (angle ORS)
angle PRS = (35) + (41)
angle PRS = 76 degrees
