Question

solve for the value of w.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((5w + 5)+(2w+8)=90\).

Step2: Combine like terms

Combine \(w\) terms and constants: \(5w+2w+5 + 8=90\), 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:

\(w = 11\)