Question

solve for the value of m.

answer

Explanation:

Step1: Set up the equation

Since the two angles are complementary (they form a right - angle, sum to \(90^{\circ}\)), we have \((8m + 7)+(5m + 5)=90\).

Step2: Combine like terms

\(8m+5m+7 + 5=90\), which simplifies to \(13m+12 = 90\).

Step3: Isolate the term with \(m\)

Subtract \(12\) from both sides: \(13m=90 - 12\), so \(13m=78\).

Step4: Solve for \(m\)

Divide both sides by \(13\): \(m=\frac{78}{13}\).

Answer:

\(m = 6\)