Question

find the values of x & y using the relationships of the angles. round your answers the nearest tenth, if necessary.

x=

y=

Explanation:

Step1: Use the property of parallel lines and transversals (corresponding angles)

Since the lines are parallel, \(3y - 7=5x\) (corresponding angles). Also, \(5x\) and \(y\) are supplementary (linear - pair), so \(5x + y=180\).
Substitute \(5x=3y - 7\) into \(5x + y=180\).
We get \((3y - 7)+y=180\).

Step2: Solve the equation for \(y\)

Combine like terms: \(3y + y-7 = 180\), \(4y=180 + 7\), \(4y=187\), \(y=\frac{187}{4}=46.75\).

Step3: Solve for \(x\)

Substitute \(y = 46.75\) into \(5x=3y - 7\).
\(5x=3\times46.75-7\), \(5x = 140.25-7\), \(5x=133.25\), \(x=\frac{133.25}{5}=26.65\approx26.7\).

Answer:

\(x = 26.7\), \(y = 46.8\)