Angles in the Same Segment Are Equal

Q. $\text{In the given figure, if}\angle ABC={69}^{\circ }\text{and}$
$\angle ACB={31}^{\circ }.$
$\text{Then, enter the value of}\angle BDC\text{in degrees}$

1. 80

Q.

In the given figure, A, B, C, D are points on a circle centred at O.The lines AC and BD are extended to meet at P and lines AD and BC intersect at Q.Then which of the following is correct?

1. $\angle AQB=2\angle ADB$

2. $\angle APB+\angle AQB=\angle AOB$

3. $\angle APB=\angle AOB+\angle AQB$

4. $\angle APB+\angle AOB=\angle AQB$

Q.

AB is the diameter of a circle with centre O.

The value of y is ___

1. ${110}^{\circ }$

2. ${120}^{\circ }$

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

4. ${150}^{\circ }$

Q.

In the given figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE= 65°, then ∠DEC =

1. 15°
2. 25°
3. 55°
4. 35°

Q. Equal arcs of a circle subtend equal angles at the centre.

1. True
2. False

Q.

In the given figure, A, B, C, D are points on a circle centred at O.The lines AC and BD are extended to meet at P and lines AD and BC intersect at Q. Then prove that $\angle APB+\angle AQB=\angle AOB$.

Q.

Select the statements that are true.

1. $\angle CDB={49}^{\circ }$

2. $\angle ABC={43}^{\circ }$

3. $\angle ACB={88}^{\circ }$

4. $\angle ACB={28}^{\circ }$

Q.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={80}^{\circ }$ and $\angle BAC$ is ${40}^{\circ }.$ Find $\angle BCD$.

1. ${60}^{\circ }$

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

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

4. ${50}^{\circ }$

Q. The number of equal angles an arc subtends in the opposite segment is _________ .

1. zero
2. infinite
3. two
4. four

Q.

Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.

1. ${15}^{\circ }$
   

2. ${25}^{\circ }$
   

3. ${95}^{\circ }$
   

4. ${35}^{\circ }$
   

Q. Angles subtended by an arc in the same segment of the circle are equal.

1. True
2. False

Q. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={80}^{\circ },\angle BAC$ is ${40}^{\circ },$ find $\angle BCD$.

1. ${40}^{\circ }$
2. ${60}^{\circ }$
3. ${80}^{\circ }$
4. ${50}^{\circ }$

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.

AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Select the statements that are true.

1. $\therefore \angle PRB={35}^{\circ }$

2. $\therefore \angle BPQ={90}^{\circ }$

3. $\angle BPR={30}^{\circ }$

4. $\angle PBR={115}^o$