Question

solve for the value of a.

Explanation:

Step1: Identify angle relationship

The two angles \(52^\circ\) and \((8a + 6)^\circ\) are complementary (they add up to \(90^\circ\) because they form a right angle). So, we set up the equation: \(52+(8a + 6)=90\).

Step2: Simplify the left side

Combine like terms: \(52 + 6+8a=90\) which simplifies to \(58 + 8a=90\).

Step3: Solve for \(a\)

Subtract 58 from both sides: \(8a=90 - 58\) \(8a = 32\). Then divide both sides by 8: \(a=\frac{32}{8}\) \(a = 4\).

Answer:

\(a = 4\)