Question

1. lines rs and tv intersect to form angles 1, 2, 3 and 4. the measure of <2 = 130°. what are the measures of the other angles? a. m<1 = 130°: m<3 = 130°; m<4 = 130° b. m<1 = 50°: m<3 = 50°; m<4 = 130° c. m<1 = 130°: m<3 = 50°; m<4 = 50° d. m<1 = 130°: m<3 = 60°; m<4 = 60°

Explanation:

Step1: Vertical angles

Vertical angles are equal. \(\angle2\) and \(\angle1\) are vertical angles. So \(m\angle1 = m\angle2=130^{\circ}\)

Step2: Linear - pair angles

Angles in a linear - pair are supplementary (\(m\angle2 + m\angle3=180^{\circ}\)). Given \(m\angle2 = 130^{\circ}\), then \(m\angle3=180 - 130=50^{\circ}\)

Step3: Vertical angles

\(\angle3\) and \(\angle4\) are vertical angles. So \(m\angle4 = m\angle3 = 50^{\circ}\)

Answer:

C. \(m\angle1 = 130^{\circ};m\angle3 = 50^{\circ};m\angle4 = 50^{\circ}\)