Abcd Is Rectangle If В€ Bpc 124в°

ABCD is a rectangle, if ∠BPC = 124° Calculate : (i) ∠BAP (ii) ∠ADP

Answers:

Diagonals of rectangle are equal and bisect each other.
∠PBC = ∠PCB = x (say)
But ∠BPC + ∠PBC + ∠PCB = 180°
124° + x + x = 180°
2x = 180° – 124°
2x = 56°
=> x = 28°
∠PBC = 28°
But ∠PBC = ∠ADP [Alternate ∠s]
∠ADP = 28°
Again ∠APB = 180° – 124° = 56°
Also PA = PB
∠BAP = \frac { 1 }{ 2 } (180° – ∠APB)
\frac { 1 }{ 2 } x (180°- 56°) = \frac { 1 }{ 2 } x 124° = 62°
Hence (i) ∠BAP = 62° (ii) ∠ADP =28°