Question

1. find the values of x and y for which the lines are parallel. x = 79, y = 47 x = 47, y = 79 x = 58, y = 57 x = 79, y = 49

Explanation:

Step1: Use corresponding - angles property

When two lines are parallel, corresponding angles are equal. So, \(x - 5=58\).

Step2: Solve for \(x\)

Add 5 to both sides of the equation \(x - 5=58\). We get \(x=58 + 5=63\). This is incorrect. Let's use the alternate - interior angles property.
For parallel lines, the sum of the interior angles on the same side of the transversal is \(180^{\circ}\).
The angle adjacent to \((x - 5)^{\circ}\) and \(58^{\circ}\) are supplementary. Also, the angle adjacent to \((y + 1)^{\circ}\) and \(74^{\circ}\) are supplementary.
First, consider the left - hand side:
The angle adjacent to \((x - 5)^{\circ}\) and \(58^{\circ}\) gives us the equation \((x - 5)+58 = 180\) (co - interior angles).

Step3: Solve for \(x\)

\(x-5+58 = 180\), \(x+53 = 180\), \(x=180 - 53=79\).
Now consider the right - hand side:
The angle adjacent to \((y + 1)^{\circ}\) and \(74^{\circ}\) gives us the equation \((y + 1)+74=180\) (co - interior angles).

Step4: Solve for \(y\)

\(y+1 + 74=180\), \(y+75 = 180\), \(y=180 - 75=47\).

Answer:

\(x = 79,y = 47\)