In the \(xy\)-plane above, points \(A, B, C, \text{ and }D\) lie on the circle with center \(O\). The degree measures of angles \(AOC\) and \(BOD\) are each \(35\degree\). What is the radian measure of angle \(AOB\) ?

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Since half of a circle is \(180 \degree\), \(m\angle AOB\) must be \(110\degree\) .

Converting this into radians:

$$ 110 \degree \cdot \frac{\pi \text{ rad}}{180\degree} $$ $$ = \boxed{\frac{11\pi}{18}} \text{ radians} $$