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 \(180^\circ)\)
\(\Rightarrow\) \(3y+147^\circ=180^\circ\)
\(\Rightarrow\) \(3y=180^\circ-147^\circ=33^\circ\)
\(\Rightarrow\) \(y=\frac{33^\circ}3=11^\circ\)
\(\therefore\) \(x+y=63^\circ+11^\circ=74^\circ\)
