9514 1404 393
Answer:
5. x° = 38°; b° = 90°
6. m∠TSU = 110°
Step-by-step explanation:
The relationship relevant to these problems is that <em>an inscribed angle is half the measure of the arc it intercepts</em>. That is also true of the angle formed by a chord and a tangent.
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5. Angle x° intercepts an arc marked 76°, so is half its measure: 76°/2 = 38°
x° = 38°
Arc b° is intercepted by an inscribed angle of 45°, so is twice that measure.
b° = 90°
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6. Long arc SU is the remaining portion of the circle after short arc SVU is subtracted:
long arc SU = 360° -140° = 220°
Angle TSU is half that measure: 220°/2 = 110°.
m∠TSU = 110°
