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Question 23

In the given figure, PQ = PR, RS = RQ and STQR. If the exterior RPU is 140, then the measure of TSR is

a) 55
b) 40
c) 50
d) 45


Solution

Here,

1=1801401=40
Since, PQ = PR
Q=R=x    [say]
In ΔPQR,P+Q+R=180   [angle sum property of a triangle]
40+x+x=1802x=180402x=140x=70
So, Q=R=70
Given that, RS = RQ
2=3=70
In ΔSQR,2+3+4=180  [angle sum property of a triangle]
70+70+4=1804=1801404=40
Also, STQR    [given]
Now, 4=6=40   [alternate interior angles]
TSR=40

 

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