Question

In the given diagram, $O$ is the centre of the circle and $PQR$ is a straight line. The value of $x$ is

• A. ${110}^o$
• B. ${120}^o$
• C. ${130}^o$
• D. ${140}^o$

Answer 1

The correct option is C ${130}^o$

In the above figure ,

$\angle QOR=2\times \angle QMR={100}^0$......(1) (Angle made by chord on the major segment is half of angle made by it on centre .)

In $△QOR,OQ=OR\to \angle OQR=\angle ORQ$........(2)

Using (1) , (2) and angle sum property of triangle in $△QOR$

$\angle OQR=\angle ORQ={40}^0$.................(3)

Now $\angle MQP$ is the exterior angle of $△MQR$

So, $\angle MQP={50}^0+{40}^0+{40}^0={130}^0$