Question

find ( moverarc{bc} ).
( moverarc{bc} = ) ( circ )

Explanation:

Step1: Recall the property of the sum of arcs in a circle

The sum of the measures of the arcs of a circle is \(360^{\circ}\). Let \(m\overset{\frown}{BC}=x\). Then we have the equation \(84^{\circ}+126^{\circ}+54^{\circ}+x = 360^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add the known arc measures: \(84 + 126+54=264\). So the equation becomes \(264^{\circ}+x = 360^{\circ}\).

Step3: Solve for \(x\)

Subtract \(264^{\circ}\) from both sides of the equation: \(x=360^{\circ}-264^{\circ}\).

Answer:

\(96\)