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`

Answer 1

∠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°