Question

ABCD is a parallelogram. if LA =6O
then LB = ? Note 'l ;is angle). a) 60o b) oo( c) 30o( d). 120°​

Answer 1

Step-by-step explanation:

ABCD is a parallelogram, in which ∠A = 60°

⇒ ∠B = 120° [Adjacent angles of a parallelogram are supplementary]

∠C = 60° = ∠A [Opposite angles of a parallelogram are equal]

∠D = ∠B = 120° [Opposite angles of parallelogram are equal]

AP bisects ∠A ⇒ ∠DAP = ∠PAB = 30°

BP bisects ∠B ⇒ ∠CBP = ∠PBA = 60°

In ΔPAB,

∠APB = 90° [Angle sum property]

In ΔPBC,

∠BPC = 60° [Angle sum property]

In ΔADP,

∠APD = 30° [Angle sum property]

In ΔPBC,

∠BPC = ∠CBP = 60° [Linear angles are supplementary]

⇒ BC = PC [Sides opposite to equal angles of a triangle are equal] -------- (1)

In ΔADP,

∠APD = ∠DAP = 30°

⇒ AD = DP [Sides opposite to equal angles of a triangle are equal]

But AD = BC [Opposite sides of parallelogram are equal]

So, BC = DP -------- (2)

From (1) and (2), we get

DP = PC

⇒ P is the midpoint of CD.