Question

plz brainlians help me......
( ➡ don't post irrelevant answers ⬅ ) ​

Answer 1

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°.

hey here your answer

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Answer 2

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+ 21

∠A+ 21

∠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= 130°+60 °/2

=95°

∴x=95°.