Question

find the m∠puw if (overrightarrow{up}) is the angle bisector of ∠wuv and m∠vup = 3x + 6 and m∠wuv = 7x + 7. first draw and label your picture. then find x and m∠puw. x = m∠puw = (remember degrees!)

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{UP}$ is the angle - bisector of $\angle WUV$, then $m\angle VUP=m\angle P UW$ and $m\angle WUV = 2m\angle VUP$.
We know that $m\angle VUP = 3x + 6$ and $m\angle WUV=7x + 7$. So, $7x + 7=2(3x + 6)$.

Step2: Solve the equation for $x$

Expand the right - hand side of the equation: $7x + 7 = 6x+12$.
Subtract $6x$ from both sides: $7x-6x+7=6x - 6x+12$, which simplifies to $x+7 = 12$.
Subtract 7 from both sides: $x=12 - 7$.
So, $x = 5$.

Step3: Find $m\angle P UW$

Since $m\angle P UW=m\angle VUP$ and $m\angle VUP = 3x + 6$, substitute $x = 5$ into the expression for $m\angle VUP$.
$m\angle P UW=3x + 6=3\times5+6=15 + 6=21$.

Answer:

$x = 5$
$m\angle P UW=21$ degrees