Question

find the measure of ∠qtu. m∠qtu = °

Explanation:

Step1: Identify angle - relationship

$\angle QTU$ and $(7x - 2)^{\circ}$ are vertical angles, so $\angle QTU=(7x - 2)^{\circ}$. Also, $(13x - 18)^{\circ}$ and $(7x - 2)^{\circ}$ are supplementary angles (linear - pair), so $(13x - 18)+(7x - 2)=180$.

Step2: Solve the equation for x

Combine like - terms:
$$(13x+7x)+(-18 - 2)=180$$
$$20x-20 = 180$$
Add 20 to both sides:
$$20x=180 + 20$$
$$20x=200$$
Divide both sides by 20:
$$x=\frac{200}{20}=10$$

Step3: Find the measure of $\angle QTU$

Substitute $x = 10$ into the expression for $\angle QTU$:
$\angle QTU=(7x - 2)^{\circ}=(7\times10 - 2)^{\circ}$
$=(70 - 2)^{\circ}=68^{\circ}$

Answer:

$68$