Question

If m_SQL = 50°, mZSRM = 60°, find mZQSR. IR Q P S . R M 10° () 60° (D) 70° D​

Answer 1

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∘

Answer 2

Step-by-step explanation:

$\fcolorbox{red}{pink}{verified\:answer}$

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

∘