Question

In the quadrilateral ABCD, ∠ = 80 ° and ∠ = 60 °. If AP and BP are the bisectors of ∠ ∠ respectively, find the measure of ∠.

Answer 1

Answer:

The answer is 95°..

Step-by-step explanation:

AP and BP are bisectors of two adjacent angles A and B of a quadrilateral ABCD.

We know that the sum of all the angles of a quadrilateral is 360°.

⇒∠A+∠B+∠C+∠D=360°, ∠A+∠B=360°−(∠D+∠C)

∴ In △PAB;

⇒∠APB+∠PAB+∠PBA=180° [ Angle sum property ]

⇒∠APB+

2

1

∠A+

2

1

∠B=180°

∴AP and BP are the bisectors of two adjacent angles A and B.

∴2∠APB+∠A+∠B=360°

⇒2∠APB=360°−(∠A+∠B)

∴2∠APB=∠C+∠D

⇒∠APB=

2

130

o

+60

o

=95°

∴x=95°.

Hence, the answer is 95°.

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