Question

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Answer 1

9514 1404 393

Answer:

1. 110°
2. 32.5°
3. 60.5°
4. 63.5°

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°