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Question

In ΔABC, with points P and Q on sides AB and AC, respectively such that APPB=AQQC. If PQ is extended to T such that PT = BC and PB = TC, then x is equal to


A

60

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B

120

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C

75

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D

45

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Solution

The correct option is A

60



In ΔABC,
APPB=AQQC .... (By using BPT)
and PT = BC .... (Given)
Since, APPB=AQQCPQ||BCPT||BC
Also, PT = BC
PTCB is a parallelogram,
1=2 ...(i)
3=2 ...(ii) [Interior opposite angles]
In ΔAPQ and ΔCTQ,
2=3 [from Eq. (ii)]
4=5 [vertically opposite angles]
ΔAPQΔCTQ [by AA similarity]
x=PAQx=60


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