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Question

In the figure, the bisectors of A and B meet at a point. If C=100 and D=50, Find the measure of APB.


Solution

In quadrilateral ABCD,

D=50,C=100
PA and PB are the bisectors of A and B.
In quadrilateral ABCD,
A+B+C+D=360
(Sum of angles of a quadrilateral)
A+B+100+50=360A+B+150=360A+B=360=150=210
and 12A+12B=2102=105
( PA and PB are bisector of A and B respectively )
PAB+PBA=105PAB+PBA+APB=180
(Sum of angles of a triangle)
105+APB=180APB=180105=75APB=75

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