Question

In a quadrilateral ABCD if angle B = 130° and angle C=60° and the bisectors of angle A and angle D intersect at P, then angle APD=​

Answer 1

Answer:

95

Step-by-step explanation:

GIVEN

B = 130

C = 60

SOLUTION

Angle A + Angle B + Angle C + Angle D = 360

Angle A/2 + Angle B/2 + Angle C/2 + Angle D/2 = 180

Angle B/2 + Angle C/2 = 180 - (Angle A/2 + Angle D/2) - 1

In triangle APD

Angle DAP + Angle ADP + Angle APD = 180 ( Angle Sum Property )

Angle A/2 + Angle D/2 + Angle APD = 180 (Angle Bisectors)

Angle APD = 180 - (Angle A/2 + Angle D/2) - 2

From 1 and 2

Angle B/2 + Angle C/2 = Angle APD

Angle APD = 130/2 + 60/2

Angle APD = 65 + 30

Angle APD = 95

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