Question

what is the value of b?

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \((b + 40^{\circ})+(b + 5^{\circ})+(b+9^{\circ})=180^{\circ}\).

Step2: Combine like - terms

\(b + b + b+40^{\circ}+5^{\circ}+9^{\circ}=180^{\circ}\), which simplifies to \(3b + 54^{\circ}=180^{\circ}\).

Step3: Isolate the variable term

Subtract \(54^{\circ}\) from both sides: \(3b=180^{\circ}- 54^{\circ}\), so \(3b = 126^{\circ}\).

Step4: Solve for \(b\)

Divide both sides by 3: \(b=\frac{126^{\circ}}{3}=42^{\circ}\).

Answer:

\(42^{\circ}\)