Question

lines m and n are parallel. find the measure of \\(\angle a\\). image of two parallel lines m and n cut by a transversal, with one angle labeled 116° and \\(\angle a\\) to find \\(m\angle a = \boxed{?}^\circ\\)

Explanation:

Step1: Identify angle relationship

Since lines M and N are parallel, and the transversal creates a linear pair with \( \angle a \) and the \( 116^\circ \) angle, they are supplementary. So \( m\angle a + 116^\circ = 180^\circ \).

Step2: Solve for \( m\angle a \)

Subtract \( 116^\circ \) from \( 180^\circ \): \( m\angle a = 180^\circ - 116^\circ \).
\( m\angle a = 64^\circ \).

Answer:

\( 64 \)