Question 1: Calculate the angle in degrees for the sector representing 25% of a pie chart.

Answer: 90

Question 2: A pie chart shows 40% for category A. What is the angle of this sector?

Answer: 144

Question 3: A sector in a pie chart is labeled as 60°. What percentage of the whole does this sector represent?

Answer: 16.67

Question 4: If a pie chart has a sector of 30°, what percentage does it represent?

Answer: 8.33

Question 5: A pie chart is divided into 5 sectors with angles 72°, 108°, 36°, 54°, and 90°. Are these sectors correctly representing their percentages? Explain your reasoning.

Answer: No, because their angles correspond to 20%, 30%, 10%, 15%, and 25%, which do not match the given angles.

Question 6: A student calculates a sector angle as 150° for a category that should represent 20%. Identify and correct the mistake in their calculation.

Answer: The student likely calculated 150° as 20% of 360°, but 20% of 360° is actually 72°, so they overestimated the angle.

Question 7: A pie chart shows 35% for a category. What is the corresponding angle? Show your working.

Answer: 126

Question 8: Construct a sector in a circle with a 45° angle. What percentage of the whole does this sector represent?

Answer: 12.5

Question 9: A pie chart's sectors are 60°, 90°, and 150°. What percentage of the total data does the 150° sector represent?

Answer: 41.67

Question 10: Identify the common mistake when calculating angles from percentages and suggest how to avoid it.

Answer: A common mistake is miscalculating 20% of 360° as 72°; students should remember to multiply percentage by 3.6 to find the angle.

Question 11: A pie chart shows 10% for a category. Calculate the angle. Then, if the angle is mistakenly taken as 30°, identify the misconception.

Answer: The misconception is that students might think 10% corresponds to 30°, which is incorrect because 10% of 360° is 36°.

Question 12: Given a sector of 135°, what percentage of the data does it represent? Show your working.

Answer: 37.5