Answer: 65 degrees
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Step-by-step explanation:
Focus on triangle OCT. We can see that the triangle is isosceles because OT = OC are two radii of the same circle. That consequently means angles T and C are the congruent base angles (rotate the triangle to see what I mean). The base angles are opposite the congruent sides.
Since base angle C is 35 degrees, that makes base angle T this measure as well.
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We just found angle CTO is 35 degrees. Angle PTO is supplementary to this, so it is 180-35 = 145 degrees.
Now focus solely on quadrilateral PTOQ. The goal is to find angle O, aka angle QOT. We found angle T in the paragraph above and it's 145 degrees. Angle Q is 90 degrees assuming segment PR is tangent to the circle at point Q.
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Recall that for any quadrilateral, the interior angles always add to 360
let x be the measure of angle O, aka angle QOT
P+T+O+Q = 360
60+145+x+90 = 360
x+295 = 360
x = 360-295
x = 65
Therefore, angle QOT is 65 degrees