Question

what is ( moverarc{tu} )?

Explanation:

Step1: Recall the total degrees in a circle

A circle has \(360^{\circ}\).

Step2: Set up the equation

Let \(m\overarc{TU}=x\). Then \(65^{\circ}+50^{\circ}+x + 115^{\circ}=360^{\circ}\) (sum of central - angle - measures of arcs in a circle).

Step3: Simplify the left - hand side

\(65 + 50+115+x=(65 + 115)+50+x=180 + 50+x=230+x\).

Step4: Solve for \(x\)

\(230+x = 360\). Subtract \(230\) from both sides: \(x=360 - 230\).

Answer:

\(130\)