Question

In figure, if lines PQ and RS intersect at point T, such that angle PRT=45°,angle RPT=95° and Angle TSQ=75°, find angle SQT​

Answer 1

Answer:

here is the answer of ur question

Answer 2

GIVEN:-

$\large\sf{PQ||SR}$

$\large\sf{\angle{PRT}=40°}$

$\large\sf{\angle{RPT}=95°}$

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$\implies$$\large\sf{\angle{PRT}+\angle{RTP}+\angle{TPR}=180°}$

$\implies$$\large\sf{40°+\angle{RTP}+95°=180°}$

$\implies$$\large\sf{\angle{RTP}+135°=180°}$

$\implies$$\large\sf{\angle{RTP}=180°-135°}$

$\implies$$\large\sf{\angle{RTP}=45°}$

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$\large\sf{\angle{PRT}=\angle{TSQ}(V.O.A)}$

$\therefore$$\large\sf{\angle{PRT}=45°}$

$\large\sf{Then,\angle{TSQ}=45°}$

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$\huge\sf\red{In\:∆TSQ,}$

$\implies$$\large\sf{\angle{SQT}+\angle{TSQ}+\angle{STQ}=180°}$

$\implies$$\large\sf{45°+75°+\angle{STQ}=180°}$

$\implies$$\large\sf{\angle{STQ}+120°=180°}$

$\implies$$\large\sf{\angle{STQ}=60°}$