Question

stairs julie is building this staircase with a rail. what measure of ∠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 parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^{\circ}\)). Here, the rail and the bottom of the staircase are the parallel lines, and the vertical part is the transversal.
Let \(\angle1\) and \(47^{\circ}\) be the consecutive - interior angles. So, \(\angle1 + 47^{\circ}=180^{\circ}\)

Step2: Solve for \(\angle1\)

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

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Answer:

\(133^{\circ}\)