Question

If lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠RPT = 95° and ∠TSQ= 75°, find ∠SQT. In Fig. 6.42.

Answer 1

IN ΔPRT

∠PRT+∠RTP+∠TPR=180°(∠s SUM PROPERTY)

40°+∠RTP+95°=180°

∠RTP=45°

NOW , ∠RTP=∠QST=45°(VERTICALLY OPPOSITE ∠s)

NOW , IN ΔQST

∠T+∠Q+∠S=180°

45°+∠Q+75°=180°

∠Q=60°

Answer 2

Answer:

Step-by-step explanation:

IN ΔPRT

∠PRT+∠RTP+∠TPR=180°(∠s SUM PROPERTY)

40°+∠RTP+95°=180°

∠RTP=45°

NOW , ∠RTP=∠QST=45°(VERTICALLY OPPOSITE ∠s)

NOW , In ΔQST

∠T+∠Q+∠S=180°

45°+∠Q+75°=180°

∠Q=60°

Hence,∠Q=60°