ICSE-VIII-Mathematics

17: Special Types of Quadrilaterals Class 8 Maths

with Solutions -
  • #5
    ABCD is a rectangle, if ∠BPC = 124°
    Calculate: (i) ∠BAP (ii) ∠ADP
    Ans : 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 = 1/2 (180° - ∠APB)
    = 1/2 ×(180°- 56°)= 1/2 ×124° = 62°
    Hence (i) ∠BAP = 62° (ii) ∠ADP = 28°