Question

find the m∠tsu if $overrightarrow{su}$ is the angle bisector of ∠tsv and m∠tsu = y + 24 and m∠usv = 4y - 18.
y =
m∠tsu =

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{SU}$ is the angle - bisector of $\angle TSV$, then $m\angle TSU=m\angle USV$. So we set up the equation $y + 24=4y-18$.

Step2: Solve the equation for $y$

Subtract $y$ from both sides: $24 = 3y-18$. Then add 18 to both sides: $24 + 18=3y$, so $42 = 3y$. Divide both sides by 3: $y=\frac{42}{3}=14$.

Step3: Find $m\angle TSU$

Substitute $y = 14$ into the expression for $m\angle TSU$. We get $m\angle TSU=y + 24=14 + 24=38$.

Answer:

$y = 14$
$m\angle TSU=38$