In the picture aside, if AP and DP are the bisectors of ∠BAD and ∠ADC respectively of the parallelogram ABCD, then by calculating let us write the value of ∠APD.

Given ABCD is Parallelogram

⇒ ∠DAB + ∠CDA = 180° (sum of adjacent angles of a Parallelogram is 180°)

Dividing the above equation by 2 on both the sides

………………eq(1)

Since AP and DP are the bisectors of ∠DAB and ∠CDA respectively

⇒ ∠PAB = ∠PAD = 1/2 ∠BAD

And ∠PDC = ∠PDA = 1/2 ∠CDA

Putting these values in eq(1)

∠PAD + ∠PDA = 90°

In triangle PAD

∠PAD + ∠PDA + ∠APD = 180°. (Angle sum property of a triangle)

⇒90° + ∠APD = 180 °

⇒∠APD = 90°