Circle rolling on another circle

Geometry Level 4

The animation shown above depicts the green circle of radius \( 5 \) rolling on the big red circle of radius \( 10 \). A radial line connecting the center of the small circle to the initial touching point is drawn in blue. If this radial line rotates through \( 360^{\circ} \), during a particular roll, what is the measure (in degrees) of the arc of the big red circle that was swept by this roll ?

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