In the following figure, P and Q are centres of two circles. The circles are intersecting at points A and B. PA produced on both the sides meets the circles at C and D. If ∠CPB = 100°, then find the value of x.

Solution (By Examveda Team)

∠CPB = 100°
AB draw,
PA = PB = Radius
∴ ∠PAB = ∠PBA
∠CPB = ∠PAB + ∠PBA (Exterior angle)
⇒ 2∠PAB = 100°
∴ ∠PAB = 50°
∠BAD = 180° - 50° = 30°
Reflex ∠BQD = 2 × 130° = 260°
∴ x = 360° - 260° = 100°