Angles in the Same Segment

Q. In the given figure, $\angle ABC={69}^{\circ }$ and $\angle ACB={31}^{\circ }.$ Find $\angle BDC.$

1. ${60}^{\circ }$
2. ${70}^{\circ }$
3. ${100}^{\circ }$
4. ${80}^{\circ }$

Q.

What are cyclic quadrilateral theorems?

Q.

Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.

Reason: Angles in the same segment are equal.


Which of the following options is correct?

1. Both the assertion and reason are true, but reason is not the correct explanation for assertion.

2. Assertion is true, but reason is false.

3. Assertion is false, but reason is true.

4. Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

Q.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ }$ and $\angle BAC={30}^{\circ }$, then $\angle BCD$= ___.

1. ${120}^{\circ }$
2. ${110}^{\circ }$
3. ${100}^{\circ }$
4. ${80}^{\circ }$

Q.

Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral ABCD is also cyclic. [4 MARKS]

Q.

In the given figure, O is the centre of the circle. If ∠ABD = 30° and ∠BAC = 80° , find ∠ACB.

[2 Marks]

Q.

Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.

Reason: Angles in the same segment are equal.


Which of the following options is correct?

1. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
2. Assertion is false but Reason is true.
3. Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
4. Assertion is true but Reason is false.

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

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

Q. If ABCD is a cyclic quadrilateral and $\angle A=120°-x°,$ then $\angle C=$ .

1. 60° + x°
2. 90° + x°
3. 60° - x°
4. 90° - x°

Q. If ABCD is a cyclic quadrilateral and $\angle A={90}^{\circ }-x^{\circ }$ , then $\angle C=$

1. 90o - xo
2. 90o+xo
3. 180o - xo
4. 90o + xo2

Q.

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

1. ${30}^{\circ }$
2. ${40}^{\circ }$
3. ${50}^{\circ }$
4. ${60}^{\circ }$

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

Q. If ABCD is a cyclic quadrilateral and $\angle A={90}^{\circ }-x^{\circ }$ , then $\angle C=$

1. 90o+xo
2. 90o - xo
3. 180o - xo
4. 90o + xo2

Q.

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

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

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

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

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

Q.
In the above figure, $p$ = __ and $q$ = ___.

1. ${40}^{\circ },{52}^{\circ }$
2. ${52}^{\circ },{40}^{\circ }$
3. ${50}^{\circ },{38}^{\circ }$
4. ${38}^{\circ },{50}^{\circ }$

Q. Consider the below figure. Here, $z$ = ___.

1. ${45}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$
4. ${15}^{\circ }$

Q.

If a side of a cyclic quadrilateral is produced, then prove that the exterior angle is equal to the interior opposite angle. [3 MARKS]

Q.

If a pair of opposite sides of a cylic quadrilateral are equal, prove that its diagonals are equal. [3 MARKS]

Q. Angles in the same segment of the circle are not equal.

1. False
2. True

Q.
If $\angle BCD={50}^{\circ },$ then $\angle BAD$ = ___.

1. ${50}^{\circ }$
2. ${100}^{\circ }$
3. ${25}^{\circ }$
4. ${70}^{\circ }$

Q.
If $\angle BCD={50}^{\circ },$ then $\angle BAD$ = ___.

1. ${50}^{\circ }$
2. ${100}^{\circ }$
3. ${25}^{\circ }$
4. ${70}^{\circ }$

Q.
In the above figure, $p$ = __ and $q$ = ___.

1. ${40}^{\circ },{52}^{\circ }$
2. ${52}^{\circ },{40}^{\circ }$
3. ${38}^{\circ },{50}^{\circ }$
4. ${50}^{\circ },{38}^{\circ }$

Q. In the given figure, $\angle ABC={69}^{\circ }$ and $\angle ACB={31}^{\circ }.$ Find $\angle BDC.$

1. ${60}^{\circ }$
2. ${70}^{\circ }$
3. ${100}^{\circ }$
4. ${80}^{\circ }$

Q. If ABCD is a cyclic quadrilateral and $\angle A={90}^{\circ }-x^{\circ }$ , then $\angle C=$

1. 180o - xo
2. 90o+xo
3. 90o - xo
4. 90o + xo2