InterviewSolution
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InterviewSolution
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From the adjacent figure, PQ || RS, ∠RPQ = 52°, ∠RPS = 65°, ∠PSR = x° and ∠PRQ = 3y° + 5, then the value of x + y isA) 115° B) 137°C) 200° D) 74° |
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Answer» Correct option is (D) 74° \(\because\) \(PQ\,||\,RS\) \(\therefore\) \(x^\circ+65^\circ+52^\circ=180^\circ\) \(\Rightarrow\) \(x^\circ=180^\circ-65^\circ-52^\circ\) \(\Rightarrow\) \(x^\circ=180^\circ-117^\circ\) \(\Rightarrow\) \(x^\circ=63^\circ\) In \(\triangle PQR,\) \(52^\circ+90^\circ+(3y+5)^\circ=180^\circ\) (Sum of interior angle in a triangle is \(180^\circ)\) \(\Rightarrow\) \(3y+147^\circ=180^\circ\) \(\Rightarrow\) \(3y=180^\circ-147^\circ=33^\circ\) \(\Rightarrow\) \(y=\frac{33^\circ}3=11^\circ\) \(\therefore\) \(x+y=63^\circ+11^\circ=74^\circ\) Correct option is D) 74° |
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