Question

⊙s ≅ ⊙x. what is the measure of the minor arc \\(\overarc{vw}\\)?
two circles, one with center x (left) and one with center s (right). in circle x, points v and w are on the circumference with a chord vw (marked congruent to chord ut in circle s). in circle s, theres an arc of 309° and chord ut. we need to find the measure of minor arc vw in circle x.
\\(m\overarc{vw} = \square^\circ\\)
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Explanation:

Step1: Recall the property of congruent circles

Since \(\odot S\cong\odot X\), their corresponding arcs are congruent if their chords are congruent. The measure of a full - circle is \(360^{\circ}\).

Step2: Calculate the measure of the minor arc \(\overparen{UT}\)

For circle \(S\), if the measure of the major arc \(\overparen{UT}\) is \(309^{\circ}\), then the measure of the minor arc \(\overparen{UT}\) is \(m\overparen{UT}=360^{\circ}- 309^{\circ}\).

$$m\overparen{UT}=360 - 309=51^{\circ}$$

Step3: Use the congruence of arcs

Because the chords \(VW\) and \(UT\) are congruent (marked with the same tick - mark) and \(\odot S\cong\odot X\), then \(m\overparen{VW}=m\overparen{UT}\)

Answer:

\(51\)