Question

Question 40

In the given figure, PQ ||ST. Then the value of x + y is

(a) ${125}^{\circ }$
(b) ${135}^{\circ }$
(c) ${145}^{\circ }$
(d) ${120}^{\circ }$

Answer 1

Since, PQ || ST, then PO will also parallel to ST.
Now, PO || ST and OS is transversal,
Therefore,
$x={85}^{\circ }$ [alternate interior angles]
Now $y+{130}^{\circ }={180}^{\circ }\left[linearpair\right]\Rightarrow y={180}^{\circ }-{130}^{\circ }\Rightarrow y={50}^{\circ }\therefore x+y={85}^{\circ }+{50}^{\circ }={135}^{\circ }$