Question

solve for the value of w.

Explanation:

Step1: Set up the equation

Since the two angles form a right - angle ($90^{\circ}$), we have $(5w + 5)+(2w+8)=90$.

Step2: Combine like terms

Combine the $w$ terms and the constant terms: $5w+2w+5 + 8=90$, which simplifies to $7w+13 = 90$.

Step3: Isolate the term with $w$

Subtract 13 from both sides: $7w=90 - 13$. So, $7w=77$.

Step4: Solve for $w$

Divide both sides by 7: $w=\frac{77}{7}$.

Answer:

$w = 11$