Question

solve for the value of r.
answer
attempt 3 out of 3
r =

Explanation:

Step1: Set up the equation

Since the two angles are complementary (they add up to \(90^{\circ}\)), we have the equation \((5r + 7)+(7r-1)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(5r+7r + 7 - 1=90\), which simplifies to \(12r+6 = 90\).

Step3: Isolate the term with \(r\)

Subtract \(6\) from both sides: \(12r+6-6=90 - 6\), so \(12r=84\).

Step4: Solve for \(r\)

Divide both sides by \(12\): \(r=\frac{84}{12}\).

Answer:

\(r = 7\)