Answer: angle PST = 129 degrees
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Explanation:
Because S and T are midpoints of segments PQ and QR, we know that ST is a midsegment of triangle PQR. Consequently, this means ST is parallel to PR.
From the same side interior angle theorem, the angles (11x-3) and (5x-9) are supplementary angles. This is only true because of the parallel lines.
So we can say the following:
(angle P) + (angle S) = 180
(5x-9) + (11x-3) = 180
(5x+11x) + (-9-3) = 180
16x - 12 = 180
16x = 180+12
16x = 192
x = 192/16
x = 12
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Use this to find angle PST
angle PST = 11x-3
angle PST = 11*12-3
angle PST = 132-3
angle PST = 129 degrees
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Optionally we can find angle QPR
angle QPR = 5x-9
angle QPR = 5*12-9
angle QPR = 60-9
angle QPR = 51 degrees
As a check, adding the two angles we found should get us 180
(angle PST)+(angle QPR) = 129+51 = 180
The answer checks out.
