Question

the parking spaces in a city lot were created by painting rows of parallel line segments, then painting a line that cuts through each of the parallel segments. a sketch of two parking spaces is shown below. if ( mangle2 = 115^{circ}), what is ( mangle1?)

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. That is, \(m\angle1 + m\angle2=180^{\circ}\).

Step2: Solve for \(m\angle1\)

We know \(m\angle2 = 115^{\circ}\). Substitute into the equation \(m\angle1+115^{\circ}=180^{\circ}\). Then \(m\angle1=180^{\circ}- 115^{\circ}\).

Answer:

\(65\)