Answer:
is the correct answer.
Step-by-step explanation:
It is given that
is the center of the circle and
.
Also it is given that arc
are <em>congruent </em>that means they make equal angles at the center
. Let the angle be
.
Also, we know that the total angle made at the center of the circle is
.
The given circle of question figure is divided in 3 arcs, so sum of angles made by all of them at the center is
.
![\Rightarrow 130 ^\circ + x +x=360^\circ\\\Rightarrow 2\times x = 230^\circ\\\Rightarrow x = 115^\circ](https://tex.z-dn.net/?f=%5CRightarrow%20130%20%5E%5Ccirc%20%2B%20x%20%2Bx%3D360%5E%5Ccirc%5C%5C%5CRightarrow%202%5Ctimes%20x%20%3D%20230%5E%5Ccirc%5C%5C%5CRightarrow%20x%20%3D%20115%5E%5Ccirc)
Hence
is the correct answer for this question.