Question

In Fig, if lines $ PQ$ and $ RS$ intersect at point $ T$, such that $ \angle PRT = 40°$, $ \angle RPT = 95°$ and $ \angle TSQ = 75°$, find $ \angle SQT$.

Answer 1

Step 1: Find $\angle RTP$

Apply angle sum property in the given triangles to find the missing angles.

In $△PRT$, by angle sum property of a triangle,

$\angle PRT+\angle RTP+\angle TPR={180}^{\circ }$

$\Rightarrow$ $40+\angle RTP+95=180$

$\Rightarrow$ $\angle RTP={45}^{\circ }$

Now angles $RTP$ and $QST$ are a pair of vertically opposite angles

$\therefore \angle RTP=\angle QTS={45}^{\circ }$

Step 2: Find $\angle SQT$

In $△SQT$, by angle sum property of a triangle

$\angle SQT+\angle STQ+\angle TSQ={180}^{\circ }$

$\Rightarrow$ $\angle SQT+{45}^{}+75={180}^{}$

$\Rightarrow$ $\angle SQT=60$

Hence, $\angle SQT$ is ${60}^{\circ }$.