Question

given that (l_1parallel l_2) and the measure of (angle c = 37^{circ}), find (mangle a) and (mangle b).
(mangle a=)
(mangle b=)

Explanation:

Step1: Identify angle - relationship

Since \(l_1\parallel l_2\), \(\angle c\) and \(\angle a\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.
So \(m\angle a=m\angle c = 37^{\circ}\)

Step2: Identify supplementary - angle relationship

\(\angle a\) and \(\angle b\) are supplementary angles (a linear - pair). The sum of the measures of two supplementary angles is \(180^{\circ}\).
So \(m\angle b=180^{\circ}-m\angle a\)
Substitute \(m\angle a = 37^{\circ}\) into the formula: \(m\angle b=180 - 37=143^{\circ}\)

Answer:

\(m\angle a = 37^{\circ}\)
\(m\angle b = 143^{\circ}\)