In the diagram given, quadrilaterals ABGF and GEDC are parallelograms, where B - G - C and F - G - E (betweenness).
Prove: mArcAB + mArcCD = 120.
Parallelograms and Circle Arc Proofs

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    First of all something about the center of the circle. Go to the midpoint of AB, draw the line L perpendicular to AB through the midpoint. This line L contains the center. Similarly go to the midpoint of CD and go up by the perpendicular line M. This line M again contains the center.
    Since AB and CD are parallel, so will be L and M....
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