Question

Lines
x
x and
y
y are parallel. If
B
=
11
x
+
20
,

G
=
7
x
+
24
B=11x+20, G=7x+24 and
E
=
1
y
+
14
E=1y+14 then find the values of
x
x and
y
y . The figure is not drawn to scale. Click Here for Help Video.





x
=
x=




y
=
y=

Answer 1

y is wrong

Answer 2

Given that the lines \( x \) and \( y \) are parallel, we can set up the equations based on the angles formed by these parallel lines and a transversal.

Let's first recognize which angles are likely involved in the equations provided. From the context of the problem involving angles \( B \), \( G \), and \( E \), we can assume that angles \( B \) and \( G \) are corresponding or alternate interior angles created by the transversal cutting through the parallel lines, making them equal to each other.

So, we equate:
\[
B = G
\]

Substituting the expressions for \( B \) and \( G \):
\[
11x + 20 = 7x + 24
\]

Now we can solve for \( x \):
1. Subtract \( 7x \) from both sides:
\[
11x - 7x + 20 = 24
\]
2. Simplify:
\[
4x + 20 = 24
\]
3. Subtract 20 from both sides:
\[
4x = 4
\]
4. Divide by 4:
\[
x = 1
\]

Next, we need to find \( y \). Since angle \( E \) must be equal to one of the angles \( B \) or \( G \) because \( y \) is also a corresponding angle, we can set it equal to \( B \):
\[
E = B
\]

Substituting the value of \( x \) into the expression for \( B \):
\[
E = 11(1) + 20 = 11 + 20 = 31
\]

Since we know the expression for \( E \) is \( 1y + 14 \), we can equate this to \( 31 \):
\[
1y + 14 = 31
\]

Now solve for \( y \):
1. Subtract 14 from both sides:
\[
1y = 17
\]
2. Thus,
\[
y = 17
\]

So we have determined the values of \( x \) and \( y \):
\[
\boxed{x = 1}
\]
\[
\boxed{y = 17}
\]

Answer 3

Let’s double-check the calculations for \( y \).

We know that:
\[
E = 1y + 14
\]

We previously calculated \( B \):
\[
B = 11x + 20
\]
Substituting \( x = 1 \):
\[
B = 11(1) + 20 = 11 + 20 = 31
\]

Since the lines are parallel, we can set \( E \) equal to \( B \):
\[
E = B
\]
Thus:
\[
1y + 14 = 31
\]

Now we solve for \( y \):
1. Subtract 14 from both sides:
\[
1y = 31 - 14
\]
\[
1y = 17
\]

Thus, we find:
\[
y = 17
\]

If the context provided indicates that this relationship is incorrect or if there's another angle involving \( y \), please provide that information.

Based on our calculations:
\[
\boxed{x = 1}
\]
\[
\boxed{y = 17}
\]

If there is additional information or another angle that needs to be considered, please let me know!