CPM Homework Help : INT2 Problem 6-24

Use the information given for each diagram below to solve for $x$ . Show all work.

$\overrightarrow{ B D }$ bisects $∠ABC$ . (Remember that an angle bisector divides the angle into two congruent angles.) If $m∠ABD = 5x - 10^\circ$ and $m∠ABC = 65^\circ$ , solve for $x$ .
Step (a):
$2(5x - 10^\circ) = 65^\circ$

Angle A, B, C with line B, D between.

Point $M$ is a midpoint of $\overline{EF}$ . If $EM = 4x - 2$ and $MF = 3x + 9$ , solve for $x$ .
Hint (b):
If $M$ is the midpoint, how are $\overline{EM}$ and $\overline{MF}$ related?

Line segment, left endpoint labeled, e, right end point labeled, f, and point between labeled, f.

$WXYZ$ at right is a parallelogram. If $m∠W = 9x - 3^\circ$ and $m∠Z = 3x + 15^\circ$ , solve for $x$ .
Hint (c):
How are the angles of the parallelogram related?