Question

solve for the value of w.

Explanation:

Step1: Set up equation

Since the two angles are complementary (they form a right - angle, sum to 90°), we have the equation $(4w - 7)+(7w - 2)=90$.

Step2: Combine like terms

$4w+7w-7 - 2=90$, which simplifies to $11w-9 = 90$.

Step3: Add 9 to both sides

$11w-9 + 9=90 + 9$, so $11w=99$.

Step4: Divide both sides by 11

$\frac{11w}{11}=\frac{99}{11}$, then $w = 9$.

Answer:

$w = 9$