The problem asks us to find the value of $b$ in the given diagram. The diagram shows a circle divided into sectors. One sector has an angle of $162^{\circ}$, and the remaining part of the circle is divided into three equal sectors, each with an angle of $b$.

1. Problem Description

The problem asks us to find the value of $b$ in the given diagram. The diagram shows a circle divided into sectors. One sector has an angle of $162^{\circ}$, and the remaining part of the circle is divided into three equal sectors, each with an angle of $b$.

2. Solution Steps

The sum of the angles in a circle is $360^{\circ}$. The circle is divided into four sectors with angles $162^{\circ}$, $b$, $b$, and $b$.

So, the sum of the angles is given by:

$162 + b + b + b = 360$

$162 + 3b = 360$

Subtract 162 from both sides of the equation:

$3b = 360 - 162$

$3b = 198$

Divide both sides of the equation by 3:

$b = \frac{198}{3}$

$b = 66$

3. Final Answer

The value of $b$ is 66.