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Each angle of a regular decagon (10 sides) is 144°. Two decagons meet at a point. What angle is left, and can a regular pentagon (108°) fill it?

Class 7Tiling PatternsGeometry
  • A36°; no, it is too big
  • B72°; yes, it fits
  • C72°; no, 108° is too big
  • D144°; yes, it fits

Step-by-Step Solution

° = 288°, so 360° − 288° = 72° is left. A pentagon's 108° corner is larger than 72°, so it would overlap.
Answer: C) 72°; no, 108° is too big

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