Question

solve for the value of b.

Explanation:

Step1: Set up the equation

Since the two angles are complementary (they form a right - angle, so their sum is \(90^{\circ}\)), we have \((7b - 8)+(6b + 7)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(7b+6b-8 + 7=90\), which simplifies to \(13b-1 = 90\).

Step3: Solve for \(b\)

Add \(1\) to both sides: \(13b=90 + 1\), so \(13b=91\). Then divide both sides by \(13\): \(b=\frac{91}{13}\).

Answer:

\(b = 7\)