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

Question

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] · Answer 1 · 2022-03-17T19:09:45+03:00

nikdorinn [45]3 years ago

8 0

Answer:

B. 12

Step-by-step explanation:

Paul [167] · Answer 2 · 2022-03-17T17:22:52+03:00

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}.
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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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