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: $130^{\circ}$
Correct Answer: $150^{\circ}$
Solution : Given: $\angle PQO=30^{\circ}$ and $\angle QRO=45^{\circ}$ Since $OQ$ and $OR$ is the radius, So, $\angle OQR=45^{\circ}$ $⇒\angle POR=2(\angle PQO+\angle OQR)$ (By angle subtended by minor arc.) $\therefore \angle POR=2(30^{\circ}+45^{\circ})=2×75^{\circ}=150^\circ$ Hence, the correct answer is $150^\circ$.
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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: $40^{\circ}$
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 : In the given figure, O is the centre of the circle, $\angle PQR=100^{\circ}$ and $\angle STR=105^{\circ}$. What is the value (in degree) of $\angle OSP$?
Option 1: 95
Option 2: 45
Option 3: 75
Option 4: 65
Question : Direction: The pie chart shows the breakup of the monthly expenditure of a person.
What is the central angle made by the sector of expenditure on education?
Option 1: 93.6$^\circ$
Option 2: 88.2$^\circ$
Option 3: 84.3$^\circ$
Option 4: 95.2$^\circ$
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