Question

In adjoining figure ,pq is parallel to rs . Angle pqt = 125 degree and angle rst = 155 degree the the measure of angle stq is

Answer 1

Answer:

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∘