Question

find the measure of the arc or central angle indicated. assume that lines which appear to be diameters are actual diameters.

1. ( mwidehat{uwt} )
2. ( mwidehat{gce} )

Explanation:

Step1: Calculate \(m\overarc{UWT}\)

The total degrees in a circle is \(360^{\circ}\).
\(m\overarc{UWT}=360^{\circ}- 69^{\circ}-71^{\circ}\)

Step2: Simplify the expression

\(m\overarc{UWT}=360^{\circ}-140^{\circ}=220^{\circ}\)

Step3: Calculate \(m\overarc{GCB}\)

The total degrees in a circle is \(360^{\circ}\).
\(m\overarc{GCB}=360^{\circ}-64^{\circ}-62^{\circ}\)

Step4: Simplify the expression

\(m\overarc{GCB}=360^{\circ}-126^{\circ}=234^{\circ}\)

Answer:

1. \(220^{\circ}\)
2. \(234^{\circ}\)