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Question

ABCD is an isosceles trapezium in which ¯¯¯¯¯¯¯¯AB¯¯¯¯¯¯¯¯¯CD , If the bisectors of BAD and ADC intersect at P. Find APD

A
45
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B
60
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C
90
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D
120
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Solution

The correct option is C 90
Since ABCD is isosceles trapezium
So angle DAB =angle ABC =x (say)
and Angle ADC = angle DCB = y (say)
Sum of all angles of quadrilateral is 360
So x + x +y + y =360
x+y =180
Angle ADP = y2 and angle DAP =x2 (Since DP and AP are angle bisectors)
y2+x2 = 90
In triangle APD
y2+x2 + angle DPA =180
So angle DPA = 90
So correact answer is Option C


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