Theorem on Cyclic Quadrilateral and Its Converse

Q. ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If $\angle ADC={130}^{\circ }$, then find $\angle BAC$.

1. ${25}^{\circ }$
2. ${50}^{\circ }$
3. ${60}^{\circ }$
4. ${40}^{\circ }$

Q.

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $\angle$BOD = ${160}^{\circ }$, then find the measure of $\angle$BPD.

1. ${100}^{\circ }$

2. ${80}^{\circ }$

3. ${90}^{\circ }$

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

Q. In the given figure, what is the value of $x$ ?

1. ${30}^{\circ }$
2. ${20}^{\circ }$
3. ${15}^{\circ }$
4. ${10}^{\circ }$

Q.

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

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

Q.

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

1. ${90}^{\circ }$

2. ${180}^{\circ }$

3. ${360}^{\circ }$

4. ${45}^{\circ }$

Q. Which of the following pairs of opposite angles can a cyclic quadrilateral have?

1. 90° and 45°
2. 60° and 120°
3. 45° and 135°
4. 70° and 120°
5. 25° and 155°
6. 100° and 80°
7. 88° and 91°
8. 130° and 50°

Q.

In the given figure, if $\angle AOC={120}^{\circ }$, then $\angle ABC$ = _______.

1. ${100}^{\circ }$
2. ${60}^{\circ }$
3. ${50}^{\circ }$
4. ${120}^{\circ }$

Q.

In the given figure, if $\angle AOC={130}^{\circ },$ then the value of $\angle ABC$ = _______.

1. ${95}^{\circ }$

2. ${115}^{\circ }$

3. ${50}^{\circ }$

4. ${100}^{\circ }$

Q.

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

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

Q. The values of $x$ and $y$ in the below figure are ___ and ___ respectively.

1. ${25}^{\circ }$ and ${60}^{\circ }$
2. ${40}^{\circ }$ and ${60}^{\circ }$
3. ${60}^{\circ }$ and ${25}^{\circ }$
4. ${40}^{\circ }$ and ${25}^{\circ }$