Question

In the adjoining figure , PQ || RS, find the value of y.

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Answer 1

Answer:

draw a line parallel to PS

Answer 2

Refers to the attachments

First, We draw a line AB parallel to PQ.

Since, AB ll PQ and QT is a transversal.

$\therefore \: PQT \: + QTA =180 \: (co \: interior \: angles)$

$\implies \: 110 + QTA =180$

$\implies \: QTA =180 - 110 \: = 70 \:$

Since, AB ll PQ and PQ ll RS , So AB ll RS and RT is a transversal.

$\therefore \: SRT + RTB = 180 (co \: interior \: angles)$

$\implies\: 127+ RTB =180$

$\implies \: RTB =180 - 127 = 53$

Since, AB is a straight line.

QTA+y+RTB=180

70+y+53=180

y+123=180

y=180 - 123

y= 57