Question

two parallel lines are cut by a transversal as shown below. suppose m∠7 = 121°. find m∠1 and m∠4.

Explanation:

Step1: Find \(m\angle1\)

\(\angle1\) and \(\angle7\) are corresponding angles.
When two parallel lines are cut by a transversal, corresponding angles are congruent.
So \(m\angle1 = m\angle7=121^{\circ}\)

Step2: Find \(m\angle4\)

\(\angle4\) and \(\angle1\) are supplementary angles (they form a linear - pair).
The sum of measures of angles in a linear - pair is \(180^{\circ}\).
Let \(m\angle4=x\), then \(x + m\angle1=180^{\circ}\)
Substitute \(m\angle1 = 121^{\circ}\) into the equation: \(x+121^{\circ}=180^{\circ}\)
\(x=180^{\circ}-121^{\circ}=59^{\circ}\)

Answer:

\(m\angle1 = 121^{\circ}\)
\(m\angle4 = 59^{\circ}\)