Question

In the figure , if PQ ‖ RS , ∠MXQ = 1350 and ∠MYR = 400 , find ∠XMY.

Answer 1

Answer:

Please add the picture of figure.

Answer 2

Step-by-step explanation:

Draw a line AB parallel to PQ, so AB∥PQ and PQ∥RS, so AB∥RS.

It is known that the sum of two interior angles on the same side is 180∘

, therefore,

∠QXM+∠XMB=180∘

∠XMB=180∘ −135∘

∠XMB=45∘

It is also known that the alternate interior angles are equal, so,

∠BMY=∠MYR

∠BMY=40∘

Now, ∠XMY=∠XMB+∠BMY

=45∘ +40∘

=85∘