Question

1. two lines are parallel and cut by a transversal,

if \\( \angle 1 = 60 ^ { \circ } \\),
what is the value of the supplementary angle?
\\( 120 ^ { \circ } \\)
\\( 30 ^ { \circ } \\)
\\( 90 ^ { \circ } \\)
\\( 60 ^ { \circ } \\)

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). Let the supplementary angle of \(\angle1\) be \(\angle x\). Then \(\angle1+\angle x = 180^{\circ}\).

Step2: Substitute the value of \(\angle1\)

Given \(\angle1 = 60^{\circ}\), substituting into the equation \(\angle1+\angle x=180^{\circ}\), we get \(60^{\circ}+\angle x = 180^{\circ}\).

Step3: Solve for \(\angle x\)

Subtract \(60^{\circ}\) from both sides of the equation: \(\angle x=180^{\circ}- 60^{\circ}\).

Answer:

\(120^{\circ}\)