Question

find the measure of ∠qwu.
m∠qwu = □°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle RVW$ and $\angle QWU$ are vertical angles. So, $100 - 4x=106 - 7x$.

Step2: Solve the equation for x

Add $7x$ to both sides: $100 - 4x+7x=106 - 7x+7x$, which simplifies to $100 + 3x=106$. Then subtract 100 from both sides: $3x=106 - 100=6$. Divide both sides by 3: $x = 2$.

Step3: Find the measure of $\angle QWU$

Substitute $x = 2$ into the expression for $\angle QWU$ (either $100 - 4x$ or $106 - 7x$). Using $100 - 4x$, we get $100-4\times2=100 - 8 = 92$.

Answer:

$92$