Question

in circle s with the measure of minor arc \\( \overparen{rt}=70^{\circ} \\), find \\( m \angle rut \\).

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Apply the theorem

Given that the measure of the minor arc \(\overset{\frown}{RT}=70^{\circ}\), and \(\angle RUT\) is an inscribed angle that intercepts arc \(\overset{\frown}{RT}\).
By the formula \(m\angle RUT=\frac{1}{2}m\overset{\frown}{RT}\)
Substitute \(m\overset{\frown}{RT} = 70^{\circ}\) into the formula: \(m\angle RUT=\frac{1}{2}\times70^{\circ}\)

Step3: Calculate the value

\(m\angle RUT = 35^{\circ}\)

Answer:

\(35^{\circ}\)