Question

in the figure given below AP and DP are bisectors of two adjacent angles A and D of a quadrilateral ABCD . Prove that 2

Answer 1

Answer:

Step-by-step explanation:

Since, in the figure given below AP and DP are bisectors of two adjacent angles A and D of a quadrilateral ABCD, our aim is to prove that 2∠P = ∠B + ∠C.

We need to consider all the angles as shown in the picture bellow.

Thus, we have to consider the sum of all angles of a quadrilateral as 360º, then:

∠A + ∠D + ∠B + ∠C = 360º

⇔ 2∠PAD + 2∠PDA + ∠B + ∠C = 360º

⇔ 2(∠PDA + ∠PAD) + ∠B + ∠C = 360º

⇔ 2(180 - ∠P) ∠B + ∠C = 360º

⇔ 360º - 2∠P + ∠B + ∠C = 360º

⇒ 2∠P = ∠B + ∠C

Hence proved.

Answer 2

Step-by-step explanation:

HOPE IT HELPS YOU.........