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. 26. reason in the parking lot shown, all of the lines for the parking spaces should be parallel. if m∠3 = 61, what should m∠1 and m∠2 be? explain.

Explanation:

Step1: Analyze question 25

Since the supports are in parallel segments, we use the properties of parallel - lines and transversals. The angle of \(50^{\circ}\) and \(y\) are alternate - interior angles.
\[y = 50^{\circ}\]
The sum of angles on a straight - line is \(180^{\circ}\). Let's assume the straight - line containing \(x\) and the angle adjacent to the \(50^{\circ}\) angle. The adjacent angle to the \(50^{\circ}\) angle is \(180 - 50=130^{\circ}\) (linear pair). And \(x\) and this \(130^{\circ}\) angle are alternate - interior angles.
\[x = 130^{\circ}\]

Step2: Analyze question 26

Since all the lines for the parking spaces are parallel, \(\angle3\) and \(\angle1\) are corresponding angles.
\[m\angle1=m\angle3 = 61^{\circ}\]
\(\angle1\) and \(\angle2\) are supplementary angles (linear pair, since they form a straight - line).
\[m\angle2=180 - m\angle1=180 - 61=119^{\circ}\]

Answer:

For question 25: \(x = 130^{\circ}\), \(y = 50^{\circ}\)
For question 26: \(m\angle1 = 61^{\circ}\), \(m\angle2 = 119^{\circ}\)