Angle Subtended by the Arc at the Center and the Circumference

Q. Angle inscribed in a semicircle is always .

1. ${30}^{\circ }$
2. ${90}^{\circ }$
3. ${45}^{\circ }$

Q. PQRS is a cyclic quadrilateral whose diagonals intersect at A. If $\angle SQR={80}^{\circ }$ and $\angle QPR={30}^{\circ },$ then find $\angle SRQ.$

1. ${80}^{\circ }$
2. ${60}^{\circ }$
3. ${50}^{\circ }$
4. ${70}^{\circ }$

Q. Match the unknown angle $x$ in each case if O is the centre of each circle.

1. ${40}^{\circ }$
2. ${30}^{\circ }$
3. ${90}^{\circ }$

Q.

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

1. ${50}^{\circ }$

2. ${40}^{\circ }$

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

4. ${20}^{\circ }$

Q.

In the given figure, if $\angle \text{OAB}={40}^{\circ }$, then $\angle \text{ACB}$ = ___.

1. ${50}^{\circ }$

2. ${40}^{\circ }$

3. ${60}^{\circ }$

4. ${70}^{\circ }$

Q.

How many degrees are in one-half of a circle?

1. 180 degrees

2. 360 degrees

3. 90 degrees

4. 45 degrees

Q.

An equilateral triangle ABC is inscribed in a circle with centre O. Then, $\angle BOC$ is equal to ___.

1. 30${}^{\circ }$
2. 60${}^{\circ }$
3. 90${}^{\circ }$
4. 120${}^{\circ }$

Q.

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

1. ${150}^{\circ }$

2. ${30}^{\circ }$

3. ${60}^{\circ }$

4. ${90}^{\circ }$

Q. ABCD is a quadrilateral such that A is the centre of the circle passing through B, C and D. Which one of the following options is correct?

1. $\angle CBD+\angle CDB=\angle BAD$
2. $\angle CBD+\angle CDB=\frac{1}{2}\angle BAD$
3. $\angle CBD+\angle CDB=\frac{2}{3}\angle BAD$
4. $\angle CBD+\angle CDB=\frac{3}{4}\angle BAD$

Q.

In the given figure, AB is the diameter of the circle. Find the value of $x$.

1. ${30}^{\circ }$

2. ${90}^{\circ }$

3. ${45}^{\circ }$

4. ${60}^{\circ }$