Question

given ( m parallel n ), find the value of ( x ) and ( y ).

Explanation:

Step1: Find the value of \(x\)

Since \(x\) and \(130^{\circ}\) are supplementary angles (they form a linear pair), we use the formula \(x + 130^{\circ}=180^{\circ}\).

$$x=180^{\circ}- 130^{\circ}$$

$$x = 50^{\circ}$$

Step2: Find the value of \(y\)

Because \(m\parallel n\), \(y\) and \(x\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(y=x\).

$$y = 50^{\circ}$$

Answer:

\(x = 50\), \(y = 50\)