Question

Lines x and y are parallel. If B=3x+16, G=2x+29, and A=2y+17then find the values of x and y. The figure is not drawn to scale.

Answer 1

Since lines \( x \) and \( y \) are parallel, angles \( B \) and \( G \) must be equal if they are corresponding angles or alternate interior angles.

We set up the equation based on the information given:

\[
B = G
\]

Substituting the expressions for \( B \) and \( G \):

\[
3x + 16 = 2x + 29
\]

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

1. Subtract \( 2x \) from both sides:
\[
3x - 2x + 16 = 29
\]
This simplifies to:
\[
x + 16 = 29
\]

2. Next, subtract 16 from both sides:
\[
x = 29 - 16
\]
This gives:
\[
x = 13
\]

Next, we need to find the value of \( y \). The problem states angle \( A \) is related to angle \( y \), but we don't have a direct equation for \( A \) in relation to \( B \) or \( G \). Thus we assume \( A \) might relate to angles from the same transversal line which may also give an equivalent angle (if \( y \) is another angle in the context).

Unless more details specify how angle \( A \) relates to the other angles, we cannot conclude the value of \( y \) directly. However, if we are looking for standard relationships based on a transversal, then:

If \( A \) is equal to one of the angles \( B \) or \( G \), you could assert that \( A = B \) or \( A = G \) depending on the orientation. Considering \( A \) is defined in the same way and possibly as \( 2y + 17 \):

If we assume \( A = B \):
\[
2y + 17 = 3x + 16
\]

Substituting \( x = 13 \):
\[
2y + 17 = 3(13) + 16
\]
This simplifies to:
\[
2y + 17 = 39 + 16
\]
Which is:
\[
2y + 17 = 55
\]
Now, subtract 17 from both sides:
\[
2y = 55 - 17
\]
Thus:
\[
2y = 38
\]
Finally, divide by 2:
\[
y = 19
\]

We find:
\[
x = 13
\]
\[
y = 19
\]

Thus, the values of \( x \) and \( y \) are:
\[
\boxed{13} \text{ and } \boxed{19}
\]

Answer 2

y is wrong

Answer 3

Let's reevaluate the relationships given in the problem to ensure we derive \( y \) correctly.

We previously established that lines \( x \) and \( y \) are parallel, and we set the angles equal as follows:

1. **Finding \( x \)**:
\[
B = G \Rightarrow 3x + 16 = 2x + 29
\]
Subtracting \( 2x \) from both sides gives:
\[
x + 16 = 29
\]
Subtracting 16 from both sides yields:
\[
x = 13
\]

2. **Finding \( y \)**:
Now, if we need to find \( y \) using the relationship involving \( A \) (which is given as \( A = 2y + 17 \)), we must also consider that \( A \) relates in some way with either \( B \) or \( G \).

Since \( A \) does not seem to be directly equal to either angle based on the problem setup, we may need to designate another parallel property.

If \( A \) is another angle formed by the same transversal that generates equivalent angles using geometric properties, we may consider \( A \) to be supplementary or equal under some transversal relation; however, we need an established relationship.

If \( A \) is supposed to be an angle made with some other valid relationship, we need additional context.

If we assume in the standard position of a transversal, we would treat it like:

- If we ignore \( A \) and consider a transversal creating a linear pair, \( B \) and \( A \) can relate as:
\[
A + B = 180^\circ
\]
Then substituting we can derive:
- If \( 2y + 17 = 180 - (3x + 16) \) we will find:
\[
2y + 17 = 180 - (39 + 16) \text{ (because \( x = 13 \) )}
\]
let’s calculate that:
\[
2y + 17 = 180 - 55
\]
This gives:
\[
2y + 17 = 125
\]
Thus subtract 17:
\[
2y = 125 - 17
\]
Which gives:
\[
2y = 108
\]
Finally, divide by 2:
\[
y = 54
\]

In conclusion, after rectifying based on \( B \) and assuming a specific relationship relevant for calculating \( A \):

The values are:

\[
x = 13
\]
\[
y = 54
\]

So, the correct value of \( y \) is \( \boxed{54} \). Thank you for your patience!