Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle6 = 134^{circ} ). find ( mangle1 ) and ( mangle4 ).

Explanation:

Step1: Find \(m\angle 4\)

Since \(\angle4\) and \(\angle6\) are corresponding angles (parallel lines cut by a transversal), \(m\angle4 = m\angle6\).
Given \(m\angle6 = 134^{\circ}\), so \(m\angle4=134^{\circ}\).

Step2: Find \(m\angle1\)

\(\angle1\) and \(\angle4\) are supplementary angles (they form a linear - pair).
We know that if two angles \(\angle x\) and \(\angle y\) are supplementary, then \(m\angle x+m\angle y = 180^{\circ}\).
Let \(x = \angle1\) and \(y=\angle4\). Substitute \(m\angle4 = 134^{\circ}\) into \(m\angle1+m\angle4=180^{\circ}\).
We get \(m\angle1=180^{\circ}-m\angle4\).
\(m\angle1 = 180^{\circ}-134^{\circ}=46^{\circ}\).

Answer:

\(m\angle1 = 46^{\circ}\), \(m\angle4 = 134^{\circ}\)