9514 1404 393
Answer:
- 110°
- 32.5°
- 60.5°
- 63.5°
Step-by-step explanation:
1. The measure of angle 1 is half the sum of the intercepted arcs:
∠1 = (1/2)(65° +155°) = 1/2(220°)
∠1 = 110°
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2. The measure of an inscribed angle is half the measure of the intercepted arc. (This is a degenerate case of the rule in the first problem.)
∠2 = 1/2(65°)
∠2 = 32.5°
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3. The measure of the angle at a tangent is half the measure of the intercepted arc. (This is a degenerate case of the rule in the second problem.)
∠3 = 1/2(arc QS) = (1/2)(360° -155° -84°) = (1/2)121°
∠3 = 60.5°
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4. The measure of angle 4 is half the difference of the measures of the intercepted arcs. From problem 3, we know that arc QV is 56°.
∠4 = 1/2((155° +56°) -84°) = (1/2)127°
∠4 = 63.5°
