In the image, we see a pie chart depicting the distribution of students who graduated from a high school and their placement in various education programs following the university entrance exams. The programs are divided into:

• Lisans (Bachelor's) – Blue section: 90°
• Önlisans (Associate's) – Yellow section: 60°
• Açıköğretim (Open University) – Green section: 100°
• Kazanamayanlar (Those Who Failed to Get Placed) – Red section: 30°

The question at the bottom asks: "In the chart, how many graduates were placed in the indicated sections after the university exam if the total number of graduates is 360 students?"

To solve this:

1. The total number of degrees in a circle is 360°. Each degree represents $\frac{360}{360} = 1$ student.
2. We can now calculate how many students correspond to each section:

• Lisans (Bachelor's): $\frac{90}{360} \times 360 = 90$ students
• Önlisans (Associate's): $\frac{60}{360} \times 360 = 60$ students
• Açıköğretim (Open University): $\frac{100}{360} \times 360 = 100$ students
• Kazanamayanlar (Unplaced): $\frac{30}{360} \times 360 = 30$ students

The total number of graduates in each section is given in the calculation above.

Would you like any more details or further explanation on any of the steps?

Here are 5 questions related to this topic:

1. How would the results change if the total number of graduates was 480 instead of 360?
2. What percentage of students failed to get placed based on this chart?
3. If a new category were added representing military school placements, how would that impact the distribution?
4. How many students would be placed in "Önlisans" if its angle was increased by 30 degrees?
5. What mathematical principles are used to convert between degrees and students in pie charts?

Tip: In pie charts, degrees can represent different quantities, but each degree always reflects a proportional fraction of the total, making visual comparisons easy.