Question

if ray uw bisects ∠tuv, m∠tuw = 13x - 5, and m∠wuv = 7x + 31, then what is the measure of each angle? m∠tuw = m∠wuv =

Explanation:

Step1: Set up the equation

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

Step2: Solve for $x$

Subtract $7x$ from both sides: $13x-7x - 5=7x-7x + 31$, which simplifies to $6x-5 = 31$. Then add 5 to both sides: $6x-5 + 5=31 + 5$, getting $6x=36$. Divide both sides by 6: $x=\frac{36}{6}=6$.

Step3: Find $\angle TUW$

Substitute $x = 6$ into the expression for $\angle TUW$: $\angle TUW=13x - 5=13\times6-5=78 - 5=73^{\circ}$.

Step4: Find $\angle WUV$

Substitute $x = 6$ into the expression for $\angle WUV$: $\angle WUV=7x + 31=7\times6+31=42 + 31=73^{\circ}$.

Answer:

$x = 6$
$m\angle TUW=73^{\circ}$
$m\angle WUV=73^{\circ}$