Practice: Angle subtended by arc at centre and on circle

Q. Given that arc, $\text{AB}$ subtends an angle of ${40}^{\circ }$ to the center of a circle. The angle made by arc $\text{AB}$ in the remaining part of the circle is

1. ${20}^{\circ }$
2. ${80}^{\circ }$
3. ${60}^{\circ }$
4. ${100}^{\circ }$

Q. If $m\angle \text{AOC}={135}^{\circ }$, then $x=?$

1. ${22.5}^{\circ }$
2. ${45}^{\circ }$
3. ${35}^{\circ }$
4. ${60}^{\circ }$

Q.
In the figure, $O$ is the centre of the circle. Find $\angle ABC$.

1. ${160}^o$
2. ${100}^o$
3. ${90}^o$
4. ${80}^o$

Q. The theorem says that "The measure of an exterior angle of a triangle is sum of the interior opposite angles". Select the correct option from the followings

1. $\angle \text{POQ}=2\angle \text{PAQ}$
2. $\angle \text{POQ}=2\angle \text{PAB}$
3. $\angle \text{POQ}=2\angle \text{QAB}$
4. $\angle \text{POQ}=\angle \text{PAQ}$

Q. In the adjoining figure, angle subtended by the arc $\text{AB}$ at the center of smaller and bigger cirles are ${60}^{\circ }$ and ${40}^{\circ }$ respectively, then $\angle \text{CAD}$ is

1. ${80}^{\circ }$
2. ${130}^{\circ }$
3. ${120}^{\circ }$
4. ${100}^{\circ }$

Q.
In the figure, $BC$ is the diameter, $PQ$ is the tangent, $O$ is the centre of circle and $\angle BAQ={65}^o$.
Find $\angle AOC$.

1. ${25}^o$
2. ${65}^o$
3. ${50}^o$
4. ${30}^o$

Q. If $O$ is the centre of the circle, find $\angle ABC$ in the figure given below.

1. ${31}^o$
2. ${30}^o$
3. ${62}^o$
4. ${124}^o$

Q. If $\beta$ is the angle subtended at the center and $\alpha$ is the angle subtended at a point on the circumference of the circle, then $\alpha =$

1. $\beta$
2. $\frac{\beta }{2}$
3. $2\beta$
4. $3\beta$

Q. If $m\angle \text{OAB}={50}^{\circ }$, then sum of angles $x,y$ and $z$ is

1. ${170}^{\circ }$
2. ${160}^{\circ }$
3. ${150}^{\circ }$
4. ${180}^{\circ }$

Q.
In the above figure, if $O$ is the centre of the circle then which of the following is correct?

1. $x+y=z$
2. $x=y=z$
3. $x+y=2z$
4. $2(x+y)=z$

Q. In the given figure,

$O$ is the centre of the circle and $X$, $Y$ and $Z$ are points on circumferemce of the circle such that $\angle XZY={23}^o$. Then $\angle XOY$ is

1. ${23}^o$
2. ${24}^o$
3. ${30}^o$
4. ${46}^o$