9514 1404 393
Answer:
3. 41°
4. 90°
5. 70°
6. 31°
Step-by-step explanation:
The relevant relationships are ...
- a semicircle measures 180°
- an inscribed angle is half the measure of the intercepted arc
- the angle where tangents meet is the supplement of the intercepted arc
- the angle where secants meet is half the difference of the intercepted arcs
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3. ∠ADB = 1/2 arc AB = 82°/2 = 41°
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4. ∠ABD = 1/2 arc AED = 180°/2 = 90°
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5. ∠AFE = 180° -arc AE = 180° -(180° -70°) = 70°
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6. ∠ACE = 1/2(arc AE -48°) = 1/2(110° -48°) = 62°/2 = 31°
