Question

when lines intersect, they form congruent angles and supplementary angles. the measure of ∠1 is 130°. what is the measure of ∠2? m∠2 = 50 what are the measures of angles 3 and 4? m∠3 = m∠4 =

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to \(180^{\circ}\). \(\angle1\) and \(\angle3\) are supplementary. So \(m\angle1 + m\angle3=180^{\circ}\). Given \(m\angle1 = 130^{\circ}\), then \(m\angle3=180^{\circ}- 130^{\circ}\).

Step2: Calculate \(m\angle3\)

\(m\angle3 = 180 - 130=50^{\circ}\)

Step3: Use the property of supplementary angles for \(\angle2\) and \(\angle4\)

\(\angle2\) and \(\angle4\) are supplementary. \(m\angle2 + m\angle4 = 180^{\circ}\). Given \(m\angle2 = 50^{\circ}\), then \(m\angle4=180^{\circ}-50^{\circ}\)

Step4: Calculate \(m\angle4\)

\(m\angle4=180 - 50 = 130^{\circ}\)

Answer:

\(m\angle3 = 50^{\circ}\), \(m\angle4=130^{\circ}\)