Question

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

Explanation:

Step1: Use corresponding - angles property for k || j

Since k || j, the corresponding angles are equal. So, \(x + 50=x - 30\) is incorrect. We should use the fact that for parallel lines k and j, the alternate - interior angles are equal. But we can also use the property of same - side interior angles. The sum of same - side interior angles for k || j is \(180^{\circ}\). So, \((x + 50)+(x - 30)=180\).
\[

$$\begin{align*} x+50+x - 30&=180\\ 2x+20&=180\\ 2x&=180 - 20\\ 2x&=160\\ x& = 80 \end{align*}$$

\]

Step2: Use corresponding - angles property for m || n

Since m || n, and we know that one of the angles formed by the transversal with m and n is \(x-30\) and the other is y. For parallel lines m and n, corresponding angles are equal. Substitute \(x = 80\) into \(x-30\), we get \(80 - 30=50\). So \(y=x - 30\), and \(y = 50\).

Answer:

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