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galina1969 [7]
3 years ago
11

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.

Mathematics
2 answers:
nikdorinn [45]3 years ago
8 0

Answer:

B. 12

Step-by-step explanation:

Paul [167]3 years ago
3 0
Let O be the center of a circle. If <span>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}.
</span>
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}.
<span />
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