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+1 vote
4.8k views
in Triangles by (49.9k points)
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In Fig., PB = PD. The value of x is 

(a) 85° (b) 90° (c) 25° (d) 35°

1 Answer

+2 votes
by (51.6k points)
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Best answer

(c) 25o

Exterior angle of triangle is equal to sum of 2 opposite interior angles.

As BC is straight line

∠PBD + 120° = 180°

∠PBD = 180° – 120°

∠PBD = 60°

As ΔPBD is isosceles triangle and PB = PD

∴ ∠PBD = ∠PDB

⇒ ∠PDB = 60°

In ΔPSR

With exterior angle ∠PSQ equal to sum of opposite interior angles

∠PDB = ∠DPC + ∠PCD

60° = x + 35°

x = 60° – 35°

x = 25°

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