Question

Lines x and y are parallel. If B = 7x + 16, G = 5x + 24 and E = 1y + 12 then find the values of x and y. Figure is not drawn to scale

X =
Y =

Answer 1

To solve for the values of \( x \) and \( y \) given that lines \( x \) and \( y \) are parallel, we can utilize the relationships between the angles formed when a transversal intersects two parallel lines. Given the angles:

- \( B = 7x + 16 \)
- \( G = 5x + 24 \)
- \( E = 1y + 12 \)

Assuming that angles B and G are corresponding or alternate interior angles (which are equal when lines are parallel), we can set \( B \) equal to \( G \):

\[
7x + 16 = 5x + 24
\]

Let's solve for \( x \):

1. Subtract \( 5x \) from both sides:
\[
2x + 16 = 24
\]

2. Subtract \( 16 \) from both sides:
\[
2x = 8
\]

3. Divide by \( 2 \):
\[
x = 4
\]

Now that we have \( x \), we can find \( y \) using the relationship that \( E \) is also an angle related to the other angles in the same way. If we assume \( E \) corresponds to either \( B \) or \( G \) (or another relationship we have not specified), we set up the equation. Let's equate \( B \) to \( E \) for simplicity:

\[
7x + 16 = 1y + 12
\]

We already know \( x = 4 \), so substitute \( x \) into the equation:

1. Calculate \( B \):
\[
B = 7(4) + 16 = 28 + 16 = 44
\]

2. Set \( B \) equal to \( E \):
\[
44 = 1y + 12
\]

3. Solve for \( y \):
- Subtract \( 12 \) from both sides:
\[
32 = 1y
\]

- So, \( y = 32 \).

In summary, the values are:

\[
\text{X} = 4
\]
\[
\text{Y} = 32
\]