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Question
In the above figure, ∠ABC is inscribed in arc ABC.
If ∠ABC = 60°. find m ∠AOC.
Solution:
∠ABC = `1/2` m(arc AXC) ......`square`
60° = `1/2` m(arc AXC)
`square` = m(arc AXC)
But m ∠AOC = \[\boxed{m(arc ....)}\] ......(Property of central angle)
∴ m ∠AOC = `square`
Solution
∠ABC = `1/2`m (arc AXC) ...... (Inscribed angle theorem)
60° = `1/2` m (arc AXC)
120° = m (arc AXC)
But m ∠ AOC = m(arc AXC) ......(Property of central angle)
∴ m ∠AOC = 120°
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______ × 2 = m(arc AXC)
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∠AOC = ______
