Question

student name college geometry review end of mod 3 sumina 8) 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 (consecutive interior angles)

If two lines are parallel, the sum of consecutive interior angles is \(180^{\circ}\). Let the given angle be \(47^{\circ}\) and \(\angle1\) be the other consecutive interior angle.

Step2: Set up the equation

We know that \(\angle1 + 47^{\circ}=180^{\circ}\) (consecutive - interior angles for parallel lines).

Step3: Solve for \(\angle1\)

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

Answer:

\(133\)