Question

h.
x =
y =

Explanation:

Step1: Find the value of \(x\)

Since the two lines are parallel, we can use the property that alternate - interior angles are equal. Also, we know that \(3x = 46+x\) (because of the relationship between the angles formed by the transversal and parallel lines).
Subtract \(x\) from both sides: \(3x - x=46+x - x\), which gives \(2x = 46\).
Divide both sides by \(2\): \(x=\frac{46}{2}=23\).

Step2: Find the value of \(y\)

First, find the angle adjacent to \(y\). The sum of angles around a point formed by the intersection of lines: the angle adjacent to \(y\) is \(3x\). Since \(x = 23\), then \(3x=3\times23 = 69\).
We know that \(y+69 = 180\) (linear - pair of angles).
Subtract \(69\) from both sides: \(y=180 - 69=111\).

Answer:

\(x = 23\), \(y = 111\)