Question

julie is building this staircase with a rail.
what measure of \\( \angle 1 \\) will ensure that the rail is parallel to the bottom of the staircase?
\\( m \angle 1 = \\)

Explanation:

Step1: Use the property of parallel lines and transversals (consecutive interior angles)

When two lines are parallel, consecutive interior angles are supplementary. That is, if the rail is parallel to the bottom of the staircase, \(\angle1\) and \(47^{\circ}\) are consecutive interior angles.
The formula for supplementary angles is \(\angle1 + 47^{\circ}=180^{\circ}\)

Step2: Solve for \(\angle1\)

Subtract \(47^{\circ}\) from both sides of the equation \(\angle1 + 47^{\circ}=180^{\circ}\)
\(\angle1=180^{\circ}- 47^{\circ}\)
\(\angle1 = 133^{\circ}\)

Answer:

\(133\)