Question

solve for the value of b.

Explanation:

Step1: Note angle - sum property

The sum of the angles in the given figure is 180° as they form a straight - line angle. So, \((9b + 1)^{\circ}+90^{\circ}+53^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, add the non - variable angles: \(90 + 53=143\). The equation becomes \(9b+1 + 143=180\), or \(9b+144 = 180\).

Step3: Isolate the term with \(b\)

Subtract 144 from both sides of the equation: \(9b=180 - 144\). So, \(9b = 36\).

Step4: Solve for \(b\)

Divide both sides by 9: \(b=\frac{36}{9}\).

Answer:

\(b = 4\)