Question

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

Answer 1

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°