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Question

In the adjacent figure, the bisectors of A and B meet at a point P. If C=1000 and D=600, find the measure of APB.


A
100
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B
80
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C
90
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D
120
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Solution

The correct option is B 80

In quadrilateral ABCD
C=1000,D=600
A+B+C+D=3600
(Angle sum property of a quadrilateral)
A+B=3600(1000+600)
= 36001600=2000

But AP and BP are the bisectors of A and B.
12(A+B)=12×2000=1000
i.e. PAB+PBA=1000

But in ΔAPB,
PAB+PBA+APB=1800
1000+APB=1800
APB=18001000=800
Thus, APB=800

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