Question

college geometry review

1. stairs 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?

Explanation:

Step1: Use the property of parallel lines and transversals

When two lines are parallel and cut by a transversal, consecutive interior angles are supplementary (sum to \(180^{\circ}\)).
Let \(\angle1\) and the \(47^{\circ}\) angle be consecutive interior angles.
So, \(\angle1 + 47^{\circ}=180^{\circ}\)

Step2: Solve for \(\angle1\)

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

Answer:

\(133\)