Question

In the figure, given below, P and Q are the centres of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x .

Answer 1

`∠ACB = 1/2 ∠APB = 1/2 xx 150^circ = 75^circ `

(Angle at the centre is double the angle at the circumference subtended by the same chord)

∠ACB + ∠BCD = 180°

(Straight line)

`=>` ∠BCD = 180° – 75° = 105°

Also, ∠BCD = `1/2` reflex ∠BQD = `1/2 (360^circ - x)`

(Angle at the center is double the angle at the circumference subtended by the same chord)

`=> 105^circ = 180^circ - x/2`

 ∴  x = 2(180° – 105°)

= 2 × 75° 

= 150°