Problem 19 · 2009 Math Kangaroo
Hard
Geometry & Measurement
symmetry
The diagram shows a regular nonagon. What is the size of the angle marked X?
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Answer: E — 60°
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Hint 1 of 2
Each interior angle of a regular nonagon is 140 degrees; the marked angle is where two extended sides meet.
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Hint 2 of 2
Outside the nonagon those sides form an isosceles triangle - use its equal base angles.
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Approach: angle-chase the external triangle
- A regular nonagon has 140 degree interior angles, so each side turned outward makes 40 degrees.
- The two extended sides form an isosceles triangle outside the nonagon whose equal base angles are each 60 degrees.
- So X = 180 - 60 - 60 = 60 degrees.
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