Question

38. ABCD is a trapezium, CP and BP are bisectors of ZC and LB respectively. Find angle A
and angle D.
С
B
25°
30
P
D
A
If you answer it quickly then you will get 50 points and yes plz answer it quickly. ​

Answer 1

Answer:

ANSWER

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°.

Answer 2

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