Point O is the center of the circle in the figure above. What is the value of \(x\) ?

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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:

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