CPM Homework Help : GC Problem 6-50

Examine the diagram at right. Based on the information below, what statement can you make about the relationships between the lines? Be sure to justify each conclusion. Remember: each part below is a separate problem.

A transversal line, N, cuts two non-parallel lines, L, and, M. About the point of intersection, of N and L, are angles, starting at top left going clockwise, labeled as follows: R, Z, Q, and P. About the point of intersection, of N and M, are angles starting at the top left going clockwise, and labeled as follows: G, H, K, W.

$p=h$
Hint (a):
When do alternate interior angles have equal measures?
Answer (a):
If $p=h$ , then $l$ and $m$ are parallel.

$w=k$
Hint (b):
If two angles which form a straight angle are congruent, what must their measures be?
Answer (b):
$n$ is perpendicular to $m$ because $w$ and $k$ are both $90º$ .

$r=q$
Hint (c):
Under what circumstances are vertical angles congruent?

$z+k=160º$
Hint (d):
Is there anything special about angles that add up to $160º$ ?