Answers:
- ST = x = 5
- RT = y = 4
- angle R = 88 degrees
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Explanation:
I'm assuming side PQ is parallel to side RT. If so, then triangle PQS is similar to triangle TRS.
From that, we can form the proportion below to solve for x.
PT/TS = QR/RS
15/x = 9/3
15*3 = x*9
45 = 9x
9x = 45
x = 45/9
x = 5
So ST is 5 units long.
The jump from ST = 5 to PT = 15 is "times 3". The same goes from RS = 3 to QR = 9.
We move in reverse to go from PQ = 12 to RT = y = 4, i.e. we divide by 3 to go from the larger triangle's lengths to the smaller triangle's lengths.
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Since PQ is parallel to RT, this means angles Q and R are congruent. They are corresponding angles. Angle Q is 88, and so is angle R.
Side note: Similar triangles have congruent corresponding angles.
