Question

solve for the value of b.

Explanation:

Step1: Use the property of parallel lines and right - angle

Since the two lines are parallel, the sum of the angles \((b + 7)^{\circ}\), \((2b+8)^{\circ}\) and the right - angle (\(90^{\circ}\)) is \(180^{\circ}\) (because they form a straight line). So we get the equation \((b + 7)+(2b + 8)+90=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((b+2b)+(7 + 8+90)=180\), which is \(3b+105 = 180\).

Step3: Solve for \(b\)

Subtract \(105\) from both sides of the equation: \(3b=180 - 105\), so \(3b=75\). Then divide both sides by \(3\), \(b=\frac{75}{3}\).

Answer:

\(b = 25\)