Question

Lines
x
x and
y
y are parallel. If
C
=
5
x
+
20
,

G
=
1
x
+
28
C=5x+20, G=1x+28 and
D
=
1
y
+
20
D=1y+20 then find the values of
x
x and
y
y . The figure is not drawn to scale.

Answer 1

To find the values of \(x\) and \(y\) given that lines \(x\) and \(y\) are parallel, we can use the fact that corresponding angles are equal when two parallel lines are intersected by a transversal.

From the equations provided:

1. \(C = 5x + 20\)
2. \(G = 1x + 28\)
3. \(D = 1y + 20\)

We can set up the relationships based on the concept of parallel lines:

Since lines \(C\) and \(G\) are parallel, the angle corresponding to \(C\) and \(G\) should be equal:

\[
C = G
\]

Substituting \(C\) and \(G\) with their expressions:

\[
5x + 20 = 1x + 28
\]

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

1. Subtract \(1x\) from both sides:
\[
5x - 1x + 20 = 28
\]
\[
4x + 20 = 28
\]

2. Subtract \(20\) from both sides:
\[
4x = 28 - 20
\]
\[
4x = 8
\]

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

Next, since the lines \(x\) and \(y\) are also parallel, we have:

\[
C = D
\]

Substituting \(C\) and \(D\):

\[
5x + 20 = 1y + 20
\]

Replace \(x\) with the value we found:

\[
5(2) + 20 = 1y + 20
\]
\[
10 + 20 = y + 20
\]
\[
30 = y + 20
\]

Subtract \(20\) from both sides:

\[
y = 30 - 20
\]

\[
y = 10
\]

Therefore, the values of \(x\) and \(y\) are:

\[
x = 2, \quad y = 10
\]