Question

Parallel lines s and t are cut by a transversal, r, as shown.

Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are blank, blank, 1, (5 x minus 4) degrees; the angles formed with r and t are blank, blank, 94 degrees, blank.

What is the value of x to the nearest whole number?
18
20
86
94

Answer 1

To solve for the value of \(x\), we need to utilize the properties of angles formed by parallel lines cut by a transversal.

Let's label the angles formed:

1. The angles at line \(s\) from the transversal \(r\) are \(A\), \(B\), \(C\), and \(D\) in clockwise order. According to the problem, these angles are labeled as follows:

- Angle \(A\) (top left) = blank
- Angle \(B\) (top right) = blank
- Angle \(C\) (bottom right) = 1
- Angle \(D\) (bottom left) = \(5x - 4\) degrees

2. The angles at line \(t\) from the transversal \(r\) are also labeled:

- Angle \(E\) (top left) = blank
- Angle \(F\) (top right) = blank
- Angle \(G\) (bottom right) = \(94\) degrees
- Angle \(H\) (bottom left) = blank

Using the angles, we know the following:

- Angle \(C\) (1 degree) and Angle \(G\) (94 degrees) are corresponding angles because they are in the same relative position with respect to the parallel lines.
- Therefore, we can set up the equation:

\[
C + G = 180
\]

Substituting the known values:

\[
1 + 94 = 180
\]

This statement is not accurate in the way it's set up as stated, so we look at another corresponding angle property.

Since \(D\) and \(G\) are also corresponding angles, we have:

\[
D + G = 180
\]

Substituting the known values for angle \(D\) and angle \(G\):

\[
(5x - 4) + 94 = 180
\]

Solving for \(x\):

1. Combine like terms:
\[
5x - 4 + 94 = 180
\]

2. This simplifies to:
\[
5x + 90 = 180
\]

3. Subtract 90 from both sides:
\[
5x = 90
\]

4. Finally, divide by 5:
\[
x = 18
\]

Thus, the value of \(x\) to the nearest whole number is:

\[
\boxed{18}
\]