Question

in the figure, $overrightarrow{cj}$ and $overrightarrow{cr}$ are opposite rays. $overrightarrow{cp}$ bisects $angle ncw$ and $overrightarrow{cl}$ bisects $angle jcn$. if $mangle ncp = 2y + 10$ and $mangle pcw = 4y - 10$, find $mangle pcw$.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{CP}$ bisects $\angle NCW$, then $m\angle NCP=m\angle PCW$.
So, $2y + 10=4y-10$.

Step2: Solve the equation for $y$

Subtract $2y$ from both sides: $10 = 4y-2y - 10$.
$10=2y - 10$.
Add 10 to both sides: $10 + 10=2y$, so $20 = 2y$.
Divide both sides by 2: $y=\frac{20}{2}=10$.

Step3: Find $m\angle PCW$

Substitute $y = 10$ into the expression for $m\angle PCW$.
$m\angle PCW=4y-10$.
$m\angle PCW=4\times10 - 10$.
$m\angle PCW=40 - 10=30$.

Answer:

$30$