Question

in the figure below, m∠2 = 41°. find m∠1, m∠3, and m∠4

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(m\angle1 = m\angle3\) and \(m\angle2 = m\angle4\). Given \(m\angle2 = 41^{\circ}\), so \(m\angle4=41^{\circ}\).

Step2: Use linear - pair property

\(\angle1\) and \(\angle2\) form a linear pair. Since the sum of angles in a linear pair is \(180^{\circ}\), we have \(m\angle1 + m\angle2=180^{\circ}\). Substitute \(m\angle2 = 41^{\circ}\) into the equation: \(m\angle1=180^{\circ}-41^{\circ}\).

$$m\angle1 = 139^{\circ}$$

Since \(m\angle1 = m\angle3\), then \(m\angle3 = 139^{\circ}\).

Answer:

\(m\angle1 = 139^{\circ}\), \(m\angle3 = 139^{\circ}\), \(m\angle4 = 41^{\circ}\)