Question

answer attempt 1 out of 2
$w =$
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Explanation:

Step1: Use the property of complementary angles

Since the two angles \((5w + 5)^{\circ}\) and \((2w+8)^{\circ}\) are complementary (they form a right - angle, so their sum is \(90^{\circ}\)), we can write the equation \((5w + 5)+(2w + 8)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5w+2w+5 + 8=90\), which simplifies to \(7w+13 = 90\).

Step3: Solve for \(w\)

Subtract \(13\) from both sides: \(7w=90 - 13\), so \(7w=77\). Then divide both sides by \(7\): \(w=\frac{77}{7}\).

Answer:

\(11\)