Intercepted Arc

Q. If vertex C, of $\angle PCQ=x$ lies on the circle. The arms of $\angle PCQ$ intersect the circle at A and B. If m(arc AB)= 120${}^{\circ }$, then find the value of $x$ .

Q. Vertex C, of $\angle PCQ=x$ lies on the circle. The arms of $\angle PCQ$ intersect the circle at A and B. If m(arc AB)= 120${}^{\circ }$, then $x$=

1. 30${}^{\circ }$
2. 60${}^{\circ }$
3. 120${}^{\circ }$
4. 150${}^{\circ }$

Q. Vertex C, of $\angle PCQ=x$ lies on the circle. The arms of $\angle PCQ$ intersect the circle at A and B. If m(arc AB)= 120${}^{\circ }$, then $x$=

1. 60${}^{\circ }$
2. 120${}^{\circ }$
3. 30${}^{\circ }$
4. 150${}^{\circ }$

Q. Vertex C, of $\angle PCQ=x$ lies on the circle. The arms of $\angle PCQ$ intersect the circle at A and B. If m(arc AB)= 120${}^{\circ }$, then $x$=

1. 150${}^{\circ }$
2. 120${}^{\circ }$
3. 60${}^{\circ }$
4. 30${}^{\circ }$

Q.

In the following figure, what is $\angle ABD$

1. 20${}^{\circ }$

2. 60${}^{\circ }$

3. 30${}^{\circ }$

4. 50${}^{\circ }$

Q. In figure, centre of a circle is $O$. A $△PQR$ is in smaller segment. Measure of $\angle PRQ$ will be:

1. less than right angle
2. more than right angle
3. right angle
4. none of these

Q.

In the given figure, O is the centre of the circle. Find $2x$.

1. ${30}^{\circ }$
2. ${80}^{\circ }$
3. ${60}^{\circ }$
4. ${40}^{\circ }$