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Solve for the angles below. Assume that segments that appear to be tangent are tangent. Round your final answers to the nearest tenth, if necessary.

m∠NSR=______degrees
m∠RSP=______degrees

Solve for the angles below. Assume that segments that appear to be tangent are tangent-example-1
User Sachiko
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1 Answer

3 votes

Answer:

m∠NSR = 113°

m∠RSP = 67°

Explanation:

Angle formed between the intersecting chords is one half the sum of the measures of the arcs intercepted by the angles.

m∠NSR =
(1)/(2)[\text{arc}(NR)+\text{arc}(PQ)]

=
(1)/(2)(176+50)

= 113°

Since, m∠NSR + m∠RSP = 180° [Linear pair of angles are supplementary]

113° + m∠RSP = 180°

m∠RSP = 180° - 113°

= 67°

User Kristof Mols
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3.6k points