Question

In the given figure if line segments $PQ$ and $RS$ intersect at point $T$, such that $\angle PRT={40}^o,\angle RPT={95}^o$ and $\angle TSQ={75}^o$, find $\angle SQT$.

Answer 1

In $△PRT$, we have

$\angle PRT+\angle RTP+\angle RPT={180}^{\circ }$ ....(Angle sum property)

${40}^{\circ }+\angle RTP+{95}^{\circ }={180}^{\circ }\angle RTP={180}^{\circ }-{135}^{\circ }={45}^{\circ }$

$\angle STQ=\angle RTP$ .....(Vertically opposite angles )

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

In $△STQ$, wehave

$\angle STQ+\angle SQT+\angle TSQ={180}^{\circ }$ ....(Angle sum property)

${45}^{\circ }+\angle SQT+{75}^{\circ }={180}^{\circ }\angle SQT={180}^{\circ }-{120}^{\circ }={60}^{\circ }$