Problem 4 · 2024 Math Kangaroo
Medium
Geometry & Measurement
area-fraction
A kangaroo cuts a pizza into 6 pieces of equal size. After it has eaten one piece, it rearranges the remaining pieces so that the gaps between the pieces are all equally big. What is the angle in each gap?
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Answer: E — 12°
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Hint 1 of 2
The five remaining pieces still cover the same total angle they did before one was removed.
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Hint 2 of 2
Find the total angle of the 5 pieces, subtract from 360°, then split the leftover into 5 equal gaps.
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Approach: share the missing angle among the gaps
- Six equal pieces means each spans 360° ÷ 6 = 60°.
- Five pieces remain, covering 5 × 60° = 300°.
- The empty angle is 360° − 300° = 60°, split into 5 equal gaps.
- Each gap is 60° ÷ 5 = 12°.
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