$$ X Z $$ is the bisector of $$ \angle W X Y $$. If $$ m \angle W X Y=9 x+12 $$ and $$ m \angle Y X Z=6 x-6 $$, what is $$ m \angle W X Z $$ ?

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Given that $$ XZ $$ is the bisector of $$ \angle WXY $$, it means that $$ XZ $$ splits $$ \angle WXY $$ into two equal angles:
$$
m \angle WXZ = m \angle YXZ
$$

We are provided with:
$$
m \angle WXY = 9x + 12
$$
$$
m \angle YXZ = 6x - 6
$$

Since $$ XZ $$ bisects $$ \angle WXY $$, we have:
$$
6x - 6 = \frac{9x + 12}{2}
$$

Multiply both sides by 2 to eliminate the fraction:
$$
12x - 12 = 9x + 12
$$

Subtract $$ 9x $$ from both sides:
$$
3x - 12 = 12
$$

Add 12 to both sides:
$$
3x = 24
$$

Divide by 3:
$$
x = 8
$$

Now, substitute $$ x = 8 $$ back into the expression for $$ m \angle WXZ $$:
$$
m \angle WXZ = \frac{9(8) + 12}{2} = \frac{72 + 12}{2} = \frac{84}{2} = 42^\circ
$$

**Answer:** $$42^\circ$$
$$ m \angle W X Z = 42^\circ $$

is the bisector of . If
and , what is ?

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