Question

solving algebraically for unknown values
find the values of x and y that make k || j and
m || n.
x = 80
y = 50

Explanation:

Step1: Use the property of consecutive interior angles

Since \(k\parallel j\), the consecutive interior angles \((x + 50)^{\circ}\) and \((x-30)^{\circ}\) are supplementary.
So, \((x + 50)+(x - 30)=180\)

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Step2: Use the property of corresponding angles

Since \(m\parallel n\), and we know \(x = 80\). The angle \((x-30)^{\circ}\) and \(y\) are corresponding angles.
Substitute \(x = 80\) into \((x - 30)\), we get \((80-30)^{\circ}=50^{\circ}\). So \(y = 50\)

Answer:

\(x = 80\), \(y=50\)