Question

1. m || n. find the value of x and y.

a. x = 45, y = 45
b. x = 135, y = 45
c. x = 55, y = 125
d. x = 45, y = 135
e. x = 125, y = 55

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), \(x\) and the \(135^{\circ}\) angle are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(x = 135^{\circ}\).

Step2: Find the value of \(y\)

\(y\) and the \(135^{\circ}\) angle are supplementary angles (because they form a linear pair). The sum of supplementary angles is \(180^{\circ}\). So \(y=180 - 135=45^{\circ}\)

Answer:

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