solve for the value of w.

Explanation:

Step1: Set up the equation

Since the two angles are complementary (sum to 90°), we have the equation $(5w + 5)+(2w+8)=90$.

Step2: Combine like - terms

Combining the $w$ terms and the constant terms, we get $5w+2w + 5+8=90$, which simplifies to $7w+13 = 90$.

Step3: Isolate the variable term

Subtract 13 from both sides of the equation: $7w=90 - 13$, so $7w=77$.

Step4: Solve for $w$

Divide both sides by 7: $w=\frac{77}{7}=11$.

Answer:

$11$