Question

find the value of x and the value of y.
a. x = 130, y = 50
b. x = 135, y = 45
c. x = 140, y = 40
d. x = 145, y = 35

Explanation:

Step1: Use the property of adjacent angles

Since \(x + y= 180\) (adjacent angles on a straight line) and \(y + 3y=180\) (alternate - interior angles and linear - pair relationship for parallel lines).
From \(y + 3y=180\), we have \(4y = 180\).

Step2: Solve for \(y\)

Divide both sides of \(4y = 180\) by \(4\): \(y=\frac{180}{4}=45\).

Step3: Solve for \(x\)

Substitute \(y = 45\) into \(x + y=180\). Then \(x=180 - y\).
\(x=180 - 45=135\).

Answer:

B. \(x = 135,y = 45\)