Question

1. if uw bisects ∠tuv, m∠tuw = (13x - 5)° and m∠wuv = (7x + 31)°, find the value of x.

Explanation:

Step1: Use angle - bisector property

Since $UW$ bisects $\angle TUV$, then $m\angle TUW=m\angle WUV$. 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 $6x-5 = 31$.

Step3: Isolate the term with $x$

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

Step4: Find the value of $x$

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

Answer:

$x = 6$