Question

1. if $overrightarrow{uw}$ bisects $angle tuv$, $mangle tuw = 13x - 5$ and $mangle wuv = 7x + 31$, find the value of x.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{UW}$ bisects $\angle TUV$, then $m\angle TUW=m\angle WUV$. So, we set up the equation $13x - 5=7x + 31$.

Step2: Isolate the variable terms

Subtract $7x$ from both sides of the equation: $(13x-7x)-5=(7x - 7x)+31$, which simplifies to $6x-5 = 31$.

Step3: Isolate the variable

Add 5 to both sides: $6x-5 + 5=31 + 5$, getting $6x=36$.

Step4: Solve for x

Divide both sides by 6: $\frac{6x}{6}=\frac{36}{6}$, so $x = 6$.

Answer:

$x = 6$