This can be most easily thought of as a ratio equation:

(arc length for 100^{o} central angle) / (arc length of full circle) = 100^{o} / 360^{o}

And we know the arc length of the full circle is its circumference, 2πr, where r is 7.

So the above ratio equality becomes

(arc length for 100^{o} central angle) / 2π * 7 = 100^{o }/ 360^{o}

So, finally,

(arc length for 100^{o} central angle) = 100^{o }* 2π * 7 / 360^{o}

which reduces to

__35π__

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