Question

1. model with mathematics a glazier is setting supports in parallel segments to prevent glass breakage during storms. what are the values of x and y? justify your conclusions.

Explanation:

Step1: Identify angle - pair relationship for x

Since the parallel segments are cut by a transversal, and the angle marked \(50^{\circ}\) and the angle represented by \(x\) are alternate - interior angles. Alternate - interior angles are congruent when two parallel lines are cut by a transversal.
So \(x = 50^{\circ}\)

Step2: Identify angle - pair relationship for y

The angle represented by \(y\) and the \(50^{\circ}\) angle are supplementary (they form a linear pair). The sum of the measures of angles in a linear pair is \(180^{\circ}\).
So \(y=180 - 50\)
\(y = 130^{\circ}\)

Answer:

\(x = 50^{\circ}\), \(y = 130^{\circ}\)