The measure of angle s = 30 degrees, the measure of arc rs = 84 degrees and line ru is tangent to the circle at r. find m angle u.

Let O be the center of a circle. If the measure of arc RS is 84 degrees, then m∠SOR=84^{0}. The triangle SOR is isoscales (because SO=OR as radii), so m∠RSO=m∠ORS=(180^{0}-84^{0}):2=48^{0}.

Line RU is tangent to the circle in point R, this means that m∠ORU=90^{0}.
Consider the triangle SRU. m∠RSU=30^{0}  and m∠SRU=48^{0}+90^{0}=138^{0}, then m∠RUS=180^{0}-30^{0}-138^{0}=12^{0}.
ANSWER: Correct choice B - 12^{0}.

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