Question

In the following figure, PB = PD. The value of x is ______.

Options

• 85°

• 90°

• 25°

• 35°

Answer 1

In the following figure, PB = PD. The value of x is 25°.

Explanation:

∠PBE = ∠PDB + ∠BPD  ...[Exterior angle property]

⇒ 120° = ∠PDB + θ   ...(i)

Now, in ΔPBD,

∠PBD + ∠BPD + ∠PDB = 180°  ...[Angle sum property]

⇒ ∠PBD + θ + ∠PDB = 180°

⇒ ∠PBD = 180° – 120° = 60°  ...[Using (i)]

And PB = PD  ...(Given)

∵ ∠PDB = ∠PBD = 60°  ...(ii)

Now, in ΔPDC,

∠PDB = ∠DCP + ∠DPC  ...[Exterior angle property]

⇒ 60° = x + 35°  ...[Using (ii)] [∵ ∠DCP = x, ∠DPC = 35° (given)]

⇒ x = 60° – 35° = 25°