Problem 7 · 2018 Math Kangaroo
Medium
Geometry & Measurement
tiling-tessellationsymmetry
Four identical rhombuses (diamonds) and two squares are fitted together to form a regular octagon, as shown. How big are the obtuse interior angles of the rhombuses?
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Answer: A — \(135^\circ\)
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Hint 1 of 2
The four rhombuses and two squares tile a regular octagon, whose interior angle is known.
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Hint 2 of 2
Relate the rhombus obtuse angle to the octagon's corner angle.
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Approach: use the octagon's interior angle
- A regular octagon has interior angles of 135°.
- Each octagon vertex coincides with the obtuse corner of a rhombus, so that obtuse angle equals the octagon's interior angle.
- Hence the obtuse interior angle of each rhombus is 135°.
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