Question

solving algebraically for unknown values
find the values of ( x ) and ( y ) that make ( k parallel j ) and ( m parallel n ).
( x=)
( y=)

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, \((x + 50)+(x - 30)=180\).
Simplify the left - hand side: \(x+50+x - 30=2x+20\).
Then \(2x+20 = 180\).
Subtract 20 from both sides: \(2x=180 - 20=160\).
Divide both sides by 2: \(x=\frac{160}{2}=80\).

Step2: Use the property of corresponding angles

Since \(m\parallel n\) and \(k\parallel j\), \(y=(x - 30)^{\circ}\) (corresponding angles).
Substitute \(x = 80\) into \(y=x - 30\).
\(y=80-30 = 50\).

Answer:

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