In an examination worth 240 marks, a student scored 52 marks. What central…

Concept

A pie chart represents a whole by a full angle of 360°. Each category receives the same fraction of 360° as its value is of the total.

Thus, for category value v and total T, the central angle is (v/T) × 360°.

Application

1. Let v = 52 marks and T = 240 marks.

2. Substitute the values: angle = (52/240) × 360°.

3. Reduce the fraction by 4: 52/240 = 13/60.

4. Compute: (13/60) × 360° = 13 × 6° = 78°.

Cross-check

1. Convert the angle back to a fraction of the circle: 78°/360° = 13/60.

2. Apply that fraction to the total marks: 240 × 13/60 = 52.

3. This recovers the given score, so the angle is consistent.

Therefore, the corresponding central angle is 78°.