Answer:
[tex]B.\ 115^\circ[/tex] is the correct answer.
Step-by-step explanation:
It is given that [tex]O[/tex] is the center of the circle and [tex]\angle AOC = 130 ^\circ[/tex].
Also it is given that arc [tex]\frown{AB} \text{ and } \frown BC[/tex] are congruent that means they make equal angles at the center [tex]O[/tex]. Let the angle be [tex]x ^\circ[/tex].
Also, we know that the total angle made at the center of the circle is [tex]360^\circ[/tex].
The given circle of question figure is divided in 3 arcs, so sum of angles made by all of them at the center is [tex]360^\circ[/tex].
[tex]\Rightarrow 130 ^\circ + x +x=360^\circ\\\Rightarrow 2\times x = 230^\circ\\\Rightarrow x = 115^\circ[/tex]
Hence [tex]B.\ 115^\circ[/tex] is the correct answer for this question.
