Question

9 Lines x and y are parallel. If B = 7x+8, G = 5x + 24 and D x = y = 1y 14 then find the values of x and y. The figure is not drawn to scale. Click Here for Help Video.

Answer 1

To find the values of \( x \) and \( y \) from the given expressions for angles \( B \), \( G \), and \( D \) assuming that lines \( x \) and \( y \) are parallel, we first need to understand the relationships between the angles.

Since lines \( x \) and \( y \) are parallel, corresponding angles and alternate interior angles are equal.

From the expressions given:
- \( B = 7x + 8 \)
- \( G = 5x + 24 \)

Assuming that angles \( B \) and \( G \) are corresponding or alternate interior angles, we can set them equal to each other:

\[
7x + 8 = 5x + 24
\]

Now, we can solve for \( x \):

1. Subtract \( 5x \) from both sides:

\[
7x - 5x + 8 = 24
\]

2. Simplify:

\[
2x + 8 = 24
\]

3. Subtract 8 from both sides:

\[
2x = 16
\]

4. Divide both sides by 2:

\[
x = 8
\]

Now, we found that \( x = 8 \).

Next, you mentioned \( D, x = y = 1y 14 \). It seems there is some misunderstanding or a mistake in that line. However, if we interpret it as \( D = 1y + 14 \), we should find the relationship between \( D \) and the previously found angles \( B \) or \( G \).

If \( D \) is another angle related to \( B \) or \( G \) through supplementary, then:

1. Let's assume \( D = 180 - B \) (for example, if \( B \) and \( D \) are supplementary angles):

\[
D = 180 - (7x + 8)
\]
\[
D = 180 - (7(8) + 8) = 180 - (56 + 8) = 180 - 64 = 116
\]

2. If \( D = 1y + 14 \), we can set that equal to \( 116 \):

\[
1y + 14 = 116
\]

3. Now, solve for \( y \):

\[
y + 14 = 116
\]

4. Subtract 14 from both sides:

\[
y = 102
\]

Thus, the values are:

\[
x = 8 \quad \text{and} \quad y = 102
\]