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California4jx
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This question has been answered before, but here goes:
1 tells you that QR = RS, which makes QRS an isosceles triangle. This means that angles RQS and RSQ share the same measurement. Since the sum of angles in a triangle is 180, then RQS + RSQ + QRS = 180.
Say RQS = RSQ = a. Then you get that a + a + QRS = 180, so a = (180 - a)/2.
This is not enough to solve the problem though.
2 tells you that ST - UT, making SUT an isosceles triangle. Again, you have that angles UST = SUT = b and UST + SUT + STU = 180. This means that 2b + STU = 180, or b = (180 - STU)/2.
Again, this alone is insufficient.
But put the two together to find x. Notice that RSQ + x + UST = 180, or in other words that a + b + x = 180. Replace a and b to get:
(180 - a)/2 + (180 - b)/2 + x = 180
180 - (a + b)/2 + x = 180
x = (a + b)/2
But notice that a and b are actually the non-right angles of triangle PRT. This means that their sum will be 180 - (measurement of right angle) = 180 - 90 = 90.
So x = (a + b)/2 = 90/2 = 45.
Answer C.
