Question

Given: circle k(O), m arc AB = 120° m∠BCA = (x+60°) Find: x

Answer 1

Answer:

x=0

Step-by-step 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

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