Given that
The figure is like
Step-by-step explanation -
Here in the given figure, the values that are given are
angle YAQ = 136
angle ABC = 121
angle RCX = x
Since PQ is parallel to RS and Y is the transversal. Then,
angle YAQ = angle BDS = 136, as they are corresponding angles.
angle RCX = angle BCD = x, as they are vertically opposite angles.
Also, the sum of angles ABC and CBD will be 180 degrees
and the sum of angles BDC and BDS will be 180 as they both are linear pairs of angles.
ABC + CBD = 180
121 + CBD = 180
CBD = 180 - 121 = 59
And
BDC + BDS = 180
BDC + 136 = 180
BDC = 180 - 136 = 44
Now the angles of triangle are BCD, CBD, BDC and their sum is 180 degrees.
BDC + CBD + BCD = 180
44 + 59 + x = 180
x = 180 - 59 - 44 = 77
x = 77
Hence option A is correct.
Final answer -
So the final answer is 77