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In the diagram shown of circle A, segments lines UV and UT are congruent. If m arch VST = 220, then determine the measure of angle VSU. Show how you arrived at your answer.

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sqdancefan

Answer:

  35°

Step-by-step explanation:

We assume that points S, T, U, V all lie on the circle.

Inscribed angle TUV intercepts long arc VST and short arc VUT. The long arc has measure 220°, so the measure of the short arc is 360° -220° = 140°.

Since chords UV and UT are the same length, point U bisects arc VUT. That means the measure of arc VU is 140°/2 = 70°.

Inscribed angle VSU intercepts arc VU, so has half the measure of the arc:

  ∠VSU = 70°/2

  ∠VSU = 35°

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