Question

find the measures of ∠a and ∠c given that m||n
$m\angle a=\square^\circ$

Explanation:

Step1: Find ∠a via co-interior angles

Since \(m \parallel n\), the angle \(61^\circ\) and \(\angle a\) are co-interior angles, so they sum to \(180^\circ\).
\(m\angle a = 180^\circ - 61^\circ\)

Step2: Calculate ∠a value

\(m\angle a = 119^\circ\)

Step3: Find ∠c via corresponding angles

Since \(m \parallel n\), the angle \(42^\circ\) and \(\angle c\) are corresponding angles, so they are equal.
\(m\angle c = 42^\circ\)

Answer:

\(m\angle a = 119^\circ\)
\(m\angle c = 42^\circ\)