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)