Pie Chart Angle D7D839

1. **State the problem:** We need to find the central angle of the horror section in a pie chart representing the favourite film genres of 800 people. 2. **Formula for central angle:** The central angle for a category in a pie chart is given by: $$\text{Central angle} = \frac{\text{Frequency of category}}{\text{Total frequency}} \times 360^\circ$$ 3. **Identify values:** - Frequency of horror = $1$ - Total frequency = $800$ 4. **Calculate the central angle:** $$\text{Central angle} = \frac{1}{800} \times 360^\circ$$ 5. **Simplify the fraction:** $$\frac{1}{800} \times 360 = \frac{\cancel{1}}{\cancel{800}} \times 360 = \frac{360}{800}$$ 6. **Simplify the fraction further:** $$\frac{360}{800} = \frac{36}{80} = \frac{9}{20}$$ 7. **Convert to decimal:** $$\frac{9}{20} = 0.45 \times 360^\circ = 16.2^\circ$$ 8. **Final answer:** The central angle of the horror section is $16.2^\circ$.