Question

what is ( moverarc{sv} )?
( moverarc{sv} =square^circ )

Explanation:

Step1: Recall the total degrees in a circle

The sum of the measures of all central angles in a circle is \(360^{\circ}\).

Step2: Set up the equation

Let \(m\overset{\frown}{SV}=x\). Then \(130^{\circ}+65^{\circ}+x + 110^{\circ}+ \text{(measure of arc }UT\text{)}=360^{\circ}\). Since arc \(UT\) and the arc opposite to \(130^{\circ}\) (if we consider the symmetry of central - angle - arc relationship in a circle with all radii equal) is not needed as we can directly sum the known arcs and subtract from \(360^{\circ}\).

$$130 + 65+110+x=360$$

$$305+x = 360$$

Step3: Solve for \(x\)

Subtract \(305\) from both sides of the equation:

$$x=360 - 305$$

$$x = 55$$

Answer:

\(55\)