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Question
ABCD is a quadrilateral in which measures of angle D and angle C are 60 degrees, and 100 degrees respectively. If the internal bisectors of angle A and angle B meet at P, then measure of angle APB is
Options
80°
90°
100°
110°
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Solution
80°
Explanation:
Let ∠BAD = 2x and ∠ABC = 2y.
then, in quadrilateral ABCD,
∠(A + B +C +D) = 360°
2x+ 2y +100° + 60° = 360°
2 (x + y) = 200°
∴ (x + y) = 100° .............(i)
As, AP and BP are angle bisector of ∠A and ∠B respectively
Then, ∠BAP = x and ∠ABP = y.
Again in ΔAPB, the sum of angles 180°
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