Problem 11 · 2024 Math Kangaroo
Medium
Geometry & Measurement
area-fraction
Carina has baked a cake and cut it into 10 equal pieces. She ate one piece and spread the remaining pieces out evenly (see diagram). How big is the angle between two neighbouring pieces?
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Answer: B — 4°
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Hint 1 of 2
Each of the 10 original pieces still has its own pointed tip angle.
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Hint 2 of 2
Nine pieces spread evenly leave gaps; the gaps share what one missing piece's worth of angle would have been.
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Approach: share the missing piece's angle among the 9 gaps
- Ten equal pieces had tip angles of 360° ÷ 10 = 36° each.
- After eating one, the 9 remaining pieces use 9 × 36° = 324° of tips.
- The leftover 360° − 324° = 36° is split evenly into 9 gaps between neighbours.
- Each gap is 36° ÷ 9 = 4°.
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