Sum of Opposite Angles of a Cyclic Quadrilateral

Q.

ABCD is a parallelogram. If the radius of the circle is 4cm, then the length of the diagonal AC is ___.

Q.

What is the sum of either pair of opposite angles of a cyclic quadrilateral?

1. 180°

2. 45°

3. 90°

4. 360°

Q.

In the adjoining figure, if $\angle QPR={67}^{\circ }$ and $\angle SPR={72}^{\circ }$, then $\angle QRS$ is equal to

1. 41

2. 23

3. 67

4. 18

Q.

If ABCD is a cyclic quadrilateral, then $x$ = ___.

1. ${80}^{\circ }$
2. ${120}^{\circ }$
3. ${90}^{\circ }$
4. ${100}^{\circ }$

Q.

In the given figure, $\angle A={60}^{\circ }$ and $\angle ABC={80}^{\circ }$, then $\angle DPC$ and $\angle BQC$ are respectively ___.

1. 30^o

2. 40^o

3. 20^o

4. 50^o

Q.

ABCD is a cyclic quadilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ }$ and $\angle BAC={30}^{\circ }$, find $\angle BCD$. Further if AB = BC, find $\angle ECD$.

1. 70^o

2. 50^o

3. 80^o

4. 60^o

Q.

ABCD is a cyclic quadrilateral. If $\angle$BCD = 100${}^{\circ }$ and $\angle$ ABD = 70${}^{\circ }$. Find $\angle$ ADB.

1. 30°

2. 40°

3. 60°

4. 50°

Q.

In the given figure, PQRS is a cyclic quadrilateral in a circle with centre O. If $\angle PSR={130}^{\circ }$. Find $\angle QPR$.​​​​​​

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

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

3. ${40}^{\circ }$

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

Q.

In a cyclic quadrilateral if one angle is 60 degrees then the angle opposite to that is ___

1. 180 degrees

2. 120 degrees

3. 60 degrees

4. 30 degrees

Q.

The sum of opposite angles in a cyclic quadrilateral is ____ degrees.

1. 120

2. 360

3. 180

4. 90