Question

in the diagram shown, \\( \overline { a b } \parallel \overline { c d } \\).
if \\( m \angle 7 = 52 ^ { \circ } \\), then what is the measure of \\( \angle 4 \\) ?
\\( \angle 4 = \\) type your answer...

Explanation:

Step1: Find the measure of ∠5

Since \(AB\parallel CD\), \(\angle7\) and \(\angle5\) are vertical angles. Vertical angles are equal, so \(m\angle5 = m\angle7=52^{\circ}\).

Step2: Use the property of consecutive - interior angles

\(\angle4\) and \(\angle5\) are consecutive - interior angles. For parallel lines \(AB\) and \(CD\) cut by a transversal, consecutive - interior angles are supplementary. That is \(m\angle4 + m\angle5=180^{\circ}\).
Substitute \(m\angle5 = 52^{\circ}\) into the equation: \(m\angle4=180^{\circ}-m\angle5\).
\(m\angle4 = 180^{\circ}- 52^{\circ}\).

Answer:

\(128\)