Question

what is m∠w? m∠w = °

Explanation:

Step1: Recall property of cyclic quadrilateral

In a cyclic quadrilateral, opposite angles are supplementary, so $\angle U+\angle W = 180^{\circ}$.

Step2: Set up the equation

We know that $\angle U=(x + 8)^{\circ}$ and $\angle W=(x + 42)^{\circ}$. So, $(x + 8)+(x + 42)=180$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $2x+50 = 180$.

Step4: Solve for $x$

Subtract 50 from both sides: $2x=180 - 50=130$. Then divide both sides by 2: $x = 65$.

Step5: Find $m\angle W$

Substitute $x = 65$ into the expression for $\angle W$. So, $m\angle W=x + 42$. Then $m\angle W=65+42=107^{\circ}$.

Answer:

$107$