Question

In the given figure PQ || RS, $\angle MXQ={135}^o$ and $\angle MYR={40}^o$, find $\angle XMY$.

Answer 1

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

It is known that the sum of two interior angles on the same side is ${180}^{\circ }$, therefore,

$\angle QXM+\angle XMB={180}^{\circ }$

$\angle XMB={180}^{\circ }-{135}^{\circ }$

$\angle XMB={45}^{\circ }$

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

$\angle BMY=\angle MYR$

$\angle BMY={40}^{\circ }$

Now, $\angle XMY=\angle XMB+\angle BMY$

$={45}^{\circ }+{40}^{\circ }$

$={85}^{\circ }$