Observe the given graph carefully.
In a circle graph, the circle is divided into different sectors, each characterized by its central angle.
The complete circle measures 360 degrees. So the complete distribution (100% data) corresponds to 360 degrees.
In the given problem, we are concerned with the budget,
[tex]360^{\circ}=100\text{ percent budget}[/tex](a)
Consider the following,
[tex]\begin{gathered} \text{ Total budget}=360^{\circ} \\ \frac{1}{4}\times\text{ Total budget}=\frac{1}{4}\times360^{\circ}=90^{\circ} \end{gathered}[/tex]So, one-fourth of the budget will correspond to the department which covers the 90-degree sector of the circle graph.
As observed from the graph, the most suitable department under this criteria is the Engineering Department.
Thus, Engineering Department gets approximately one-fourth of the annual budget.
(b)
Consider that the departments Engineering and support combiningly cover a little more than one-third of the area of complete circle.
Consider the following,
[tex]\begin{gathered} 360^{\circ}=100\text{ percent} \\ 120^{\circ}=\frac{120}{360}\times100=33.33\text{ percent} \end{gathered}[/tex]Note that the area covered by the department is a little more than one-third, so the corresponding percentage value must also be a little more than 33.33%.
From the available options, 40% is the value available next to 33.33%, so this should be the most suitable choice.
Thus, it can be concluded that approximately 40% of the annual budget goes to the departments Engineering and Support combined.
Therefore, option (b) is the correct choice.
