Question

In the given figure, 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.

• A. ${150}^{\circ }$
• B. ${130}^{\circ }$
• C. ${120}^{\circ }$
• D. ${140}^{\circ }$

Answer 1

The correct option is B

${130}^{\circ }$

In the given figure,
$\angle APB=2\angle ACB$ [Angle subtended by an arc at the center is double the angle subtended by it at any other point on the remaining part of the circle]
$\Rightarrow \angle ACB={65}^{\circ }$

Now, $\angle ACB+\angle BCD={180}^{\circ }$ [Linear pair angles]
$\Rightarrow BCD={115}^{\circ }$
$\therefore$ Reflex$\angle BQD=2\angle BCD=2\times {115}^{\circ }={230}^{\circ }$
Also, x + Reflex$\angle BQD={360}^{\circ }$
$\Rightarrow x+{230}^{\circ }={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-{230}^{\circ }={130}^{\circ }$