Question

two parallel lines are crossed by a transversal. if m∠1=61.8°, then what is the measure of m∠6? 61.8° 81.8° 118.2° 128.2°

Explanation:

Step1: Identify angle relationships

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^\circ\)), and vertical angles/alternate interior angles have specific relationships. First, \(\angle1\) and \(\angle3\) are vertical angles? No, wait, \(\angle1\) and \(\angle4\) are supplementary? Wait, actually, \(\angle1\) and \(\angle3\) are vertical? No, let's look at the lines. Line \(x\) and \(y\) are parallel, transversal is the other line. \(\angle1\) and \(\angle5\) are corresponding angles? Wait, no, \(\angle1\) and \(\angle3\) are adjacent supplementary? Wait, \(\angle1 + \angle2 = 180^\circ\), but we need \(\angle6\). Let's see: \(\angle1\) and \(\angle3\) are vertical? No, \(\angle1\) and \(\angle4\) are supplementary? Wait, maybe \(\angle1\) and \(\angle5\) are corresponding (since \(x \parallel y\)), so \(\angle1 = \angle5\). Then \(\angle5\) and \(\angle6\) are supplementary (linear pair), so \(\angle5 + \angle6 = 180^\circ\). So \(\angle6 = 180^\circ - \angle1\).

Step2: Calculate \(m\angle6\)

Given \(m\angle1 = 61.8^\circ\), so \(m\angle6 = 180^\circ - 61.8^\circ = 118.2^\circ\).

Answer:

\(118.2^\circ\)