Question

find the measure of ∠qtu. m∠qtu =

Explanation:

Step1: Identify angle - relationship

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

Step2: Solve the equation for x

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

Step3: Find the measure of $\angle QTU$

Since $\angle QTU=(7x - 2)^{\circ}$, substitute $x = 10$ into the expression. $m\angle QTU=7\times10-2=70 - 2=68^{\circ}$.

Answer:

$68$