Question : In the given figure, $\mathrm{O}$ is the centre of the circle and $\angle\mathrm{AOB}=130^{\circ}$. Find $\angle\mathrm{APB}$.
Option 1: $110^{\circ}$
Option 2: $115^{\circ}$
Option 3: $100^{\circ}$
Option 4: $95^{\circ}$
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Correct Answer: $115^{\circ}$
Solution : Given: $\angle{AOB}=130^{\circ}$ To find $\angle{APB}$ The arc AB subtends $\angle{AOB}$ at the centre and $\angle{AQB}$ at a point Q of the remaining parts of a circle. $\therefore$ $\angle{AOB} = 2\angle{AQB}$ ⇒ $\angle{AQB} = \frac{130^\circ}{2} = 65^\circ$ In a cyclic quadrilateral, $\angle{APB}+\angle{AQB} = 180^\circ$ $\therefore$ $\angle{APB} = 180^\circ - 65^\circ = 115^\circ$ Hence, the correct answer is $115^\circ$.
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Question : In the given figure, if $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle with centre $\mathrm{O}$ such that $\angle \mathrm{APB}=54^{\circ}$, then $\angle \mathrm{OBA}=$________.
Question : In the given figure, ' $G$ ' is the centre of the circle. Find the $\angle ACB$ when $\angle AGB=132^{\circ}$.
Question : In the given figure, $O$ is the centre of the circle and $\angle AOC=140°$. Find $\angle ABC$.
Question : In the given figure, PQRS is a square and SRT is an equilateral triangle. What is the value of $\angle SOR ?$
Question : Directions: Select the option figure in which the given figure is embedded as its part (rotation is NOT allowed).
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