Question

x is the midpoint of \\( \overline { u v } \\). y is the midpoint of \\( \overline { u w } \\). if \\( m \angle u x y = 64 \\), find \\( m \angle v \\).

\\( m \angle v = \square \\)

Explanation:

Step1: Use the mid - segment theorem

Since \(X\) is the mid - point of \(UV\) and \(Y\) is the mid - point of \(UW\), by the mid - segment theorem, \(XY\parallel VW\).

Step2: Use the property of parallel lines

When \(XY\parallel VW\), \(\angle UXY\) and \(\angle V\) are corresponding angles. For parallel lines \(XY\) and \(VW\) with transversal \(UV\), we know that if two parallel lines are cut by a transversal, then corresponding angles are equal. Given \(m\angle UXY = 64^{\circ}\), so \(m\angle V=m\angle UXY\).

Answer:

\(64\)