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In the diagram below, PQ is a diameter of the circle. Find angle XYZ in degrees.

 Jan 7, 2020
 #1
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Angle XYZ is (180 - 80 - 35) + 80/2 = 105 degrees.

 Jan 7, 2020
 #2
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I figured out the answer, but i'll post it in case anybody wants to read it.

We see that arc XZ is 180-80-35=65, so angle XYZ=(180+65)/2=122.5

 Jan 7, 2020
 #3
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It's interesting that the sum of the internal angles of the shape OXYZ is equal to the angle XYZ.

                           17.5° +65° + 40° = 122.5°     indecision

 Jan 8, 2020

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