Question

Given: circle k(O), m arc AB = 120°

m∠BCA = (x+60°)

Find: x

Answer 1

x=0

Explanation:

Given circle O such that:

`mAB=120^\circ\\m\angle BCA =(x+60^\circ)`

The measure of arc AB is the measure of
`\angle AOB` which is an angle subtended by arc AB and passes through the center of the circle.

`\angle BCA` is an angle subtended by arc AB and passes through the the point C on the circle.

By the Inscribed Angle Theorem

`mAB=2 X m\angle BCA \\120^\circ=2(x+60^\circ)\\120^\circ=2x+120^\circ\\2x=120^\circ-120^\circ\\2x=0\\x=0`