9514 1404 393
Answer:
- x = 7
- y = 12
- ∠TPS = 140°
- ∠TPQ = 40°
- ∠PRS = 50°
Explanation:
The marked angles at P are a linear pair, so are supplementary:
(5x +5) +(18x+14) = 180
23x = 161 . . . . . . . . . . . . . . subtract 19
x = 7
Those angle measures are ...
∠TPQ = (5·7 +5)° = 40°
∠TPS = (18·7 +14)° = 140°
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The marked angle at R is the complement of the acute angle at P, so we have ...
3y +14 +40 = 90
3y = 36
y = 12
∠PRS = (3·12 +14)° = 50°