Question

In the given figure,PQ || RS and angle QXN =105°, angle RYN =45°, find angle XNY.​

Answer 1

Answer:

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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

∘

Answer 2

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

∘