Angles Subtended by Arc on the Same Segment

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

1. True
2. False

Q. A quadrilateral $\text{ABCD}$ is inscribed in a circle. If $\angle \text{D}={55}^{\circ }$, then the $\angle \text{E}$ is

1. ${55}^{\circ }$
2. ${125}^{\circ }$
3. ${65}^{\circ }$
4. ${145}^{\circ }$

Q. In the diagram below, there are four circles, each with an angle formed in the center and a point on the remaining part of the circle. How many circles do you think justifies the statement : "The Angles subtended by an arc in the same segment of a circle are equal."?

1. $\text{One}$
2. $\text{Two}$
3. $\text{Three}$
4. $\text{All of them}$

Q. The measure of all angles subtended by an arc on the same segment of the circle are -

1. equal
2. unequal
3. double the measure of the angle subtended at the centre by the same arc.
4. Insufficient data.

Q. For the given figure find the measure of angle ∠BEC.

degrees

Q. Consider the triangles $△BCD$ and $△ACD:$

Find the exterior angle $\angle E.$

1. ${145}^o$
2. ${150}^o$
3. ${155}^o$
4. Insufficient data.

Q. If the sum of measure of angles $\angle B,\angle A$ and $\angle E$ is ${90}^o,$ find the measure of each individual angle, i.e., $\angle B,\angle A$ and $\angle E.$

1. ${30}^o$
2. ${45}^o$
3. ${60}^o$

Q. Given $\angle DCA={20}^o$ and $\angle DEC={115}^o.$ Find the angle $\angle BAC.$

1. ${30}^o$
2. ${45}^o$
3. ${60}^o$
4. ${80}^o$

Q. In the given figure, $\text{A}$, $\text{B}$, $\text{C}$ and $\text{D}$ are four points on a circle. $\text{AC}$ and $\text{BD}$ intersect at a point $\text{E}$ such that $\angle \text{BEC}={130}^{\circ }$ and $\angle \text{ECD}={20}^{\circ }$. $\angle \text{BAC}$ is

1. ${110}^{\circ }$
2. ${130}^{\circ }$
3. ${20}^{\circ }$
4. ${150}^{\circ }$

Q. In the adjoining figure, if $\angle \text{ABC}={\text{a}}^{\circ }$ and $\angle \text{ADC}={\text{b}}^{\circ }$, then $\text{a}=$

1. $\text{b}$
2. $\text{2b}$
3. $\text{3b}$
4. $\text{4b}$