Point O is the center of the circle in the figure above. What is the value of $x$ ?

Summary Submit

If we draw a line segment from $A$ to $O$, we obtain an isosceles triangle since $AO \text{ and } BO$ are both radii of the circle. Using our knowledge of isosceles triangles, $m\angle OAB=15\degree$. We can then find $m\angle AOB=150\degree$ by summing up the angles of the triangle to $180 \degree$.

Similarly, $m\angle AOC$ will also be equal to $150\degree$. We can sum up the central angles:

$$x\degree + m\angle AOB + m\angle AOC = 360\degree$$ $$x\degree + 150\degree + 150\degree = 360 \degree$$ $$x= \boxed{60 \degree}$$