Question

metry: concepts and connections (27.0821000) yl ic (spring)
proving lines parallel
assignment active
solving algebraically for unknown values
find the values of x and y that make $k \parallel j$ and $m \parallel n$.
$x = \square^\circ$
$y = \square^\circ$
$(x + 50)^\circ$
$(x - 30)^\circ$

Explanation:

Step1: Set up equation for \(m \parallel n\)

For lines \(m\) and \(n\) to be parallel, the consecutive interior angles formed by transversal \(k\) are supplementary.
$$(x+50) + (x-30) = 180$$

Step2: Solve for \(x\)

Simplify and solve the linear equation.
$$2x + 20 = 180$$
$$2x = 160$$
$$x = 80$$

Step3: Find angle for \(k \parallel j\)

First calculate \((x-30)^\circ\) with \(x=80\):
$$(80-30)^\circ = 50^\circ$$
For \(k \parallel j\), \(y\) and \((x-30)^\circ\) are supplementary (consecutive interior angles).
$$y + 50 = 180$$

Step4: Solve for \(y\)

Isolate \(y\) to find its value.
$$y = 180 - 50 = 130$$

Answer:

$x = 80^\circ$
$y = 130^\circ$