Question

in the following figure,PQ||RS ∆MXQ=135° and ∆MYR= 40° find ∆XMY

Answer 1

Construct a parallel line of RS on point m
So, at M 2 angles are formed name it angle A and angle B
Angle B=40° because they are adjacent angles
Angle A=45° because at angle X linear pair formed 180-135=45° and it is also adjacent angle
So, A+B=M
45°+40°=85°
HOPE IT HELPS

Answer 2

Here, we need to draw a line AB parallel to line PQ, through point M

Now, AB || PQ and PQ || RS.

Therefore, AB || RS (Why?)

Now, angle QXM + angle XMB = 180°

(AB || PQ, Interior angles on the same side of the transversal XM)

But angle QXM = 135°

So, 135° + angle XMB = 180°

Therefore, angle XMB = 45° (1)

Now, angle BMY = angle MYR (AB || RS, Alternate angles)

Therefore, angle BMY = 40° (2)

Adding (1) and (2), you get

angle XMB + angle BMY = 45° + 40°

That is, angle XMY = 85°