Question : In the adjoining figure $\angle AOC=140^{\circ}$, where O is the centre of the circle then $\angle ABC$ is equal to:
Option 1: $110^{\circ}$
Option 2: $100^{\circ}$
Option 3: $90^{\circ}$
Option 4: $40^{\circ}$
Correct Answer: $110^{\circ}$
Solution : Given: $\angle AOC = 140^{\circ}$ Construction: Take D on the remaining arc. We know that, The angle formed by the chord at the centre is twice the angle formed in the same arc segment. $\angle AOC = 2\angle ADC$ ⇒ $140^{\circ} = 2\angle ADC$ $\therefore \angle ADC = 70^{\circ}$ Now, the sum of the opposite angle of the cyclic quadrilateral is $180^{\circ}$. $\angle ABC+\angle ADC=180^{\circ}$ ⇒ $\angle ABC+70^\circ=180^{\circ}$ $\therefore\angle ABC=110^{\circ}$ Hence, the correct answer is $110^{\circ}$.
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Question : In the given figure, O is the centre of the circle, $\angle PQO=30^{\circ}$ and $\angle QRO=45^{\circ}$. What is the value (in degrees) of $\angle POR$?
Option 1: $150^{\circ}$
Option 2: $110^{\circ}$
Option 3: $160^{\circ}$
Option 4: $130^{\circ}$
Question : In the given figure, O is the centre of the circle, $\angle DAB=110^{\circ}$ and $\angle BEC=100^{\circ}$. What is the value (in degrees) of $\angle OCB$?
Option 1: 5
Option 2: 10
Option 3: 15
Option 4: 20
Question : In the following figure, AB is the diameter of a circle whose centre is O. If $\angle AOE=150^{\circ},\angle DAO=51^{\circ}$ then the measure of $\angle CBE$ is:
Option 1: 115°
Option 2: 110°
Option 3: 105°
Option 4: 120°
Question : Directions: Select the figure that will come next in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Question : Directions: Select the figure that will replace the question mark (?) in the following figure series.
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