Question

In figure $PQ\parallel RS$; $\angle MXQ={135}^o$ and $\angle MYR={40}^o$, find $\angle XMY$

Answer 1

Draw a line parallel to $PQ$ and it be $ON$

$\angle MXQ=\angle OMX(\because$ alternating angles $)$

$⟹\angle OMX={135}^{\circ }⟹\angle XMN={180}^{\circ }-{135}^{\circ }={45}^{\circ }$

$\angle YMN=\angle RYM={40}^{\circ }$

$⟹\angle XMY=\angle XMN+\angle RYM={45}^{\circ }+{40}^{\circ }={85}^{\circ }$