Question

In the below figure, PQ||RS||UV. Find the value of y.​

Answer 1

Answer:

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)∴PQT+QTA=180(cointeriorangles)

\implies \: 110 + QTA =180⟹110+QTA=180

\implies \: QTA =180 - 110 \: = 70 \:⟹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)∴SRT+RTB=180(cointeriorangles)

\implies\: 127+ RTB =180⟹127+RTB=180

\implies \: RTB =180 - 127 = 53⟹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