Problem 21 · 2017 Math Kangaroo
Stretch
Geometry & Measurement
sum-constraint
If you measure the angles of a triangle, you obtain three different natural numbers. What is the smallest possible sum of the biggest and the smallest angle of the triangle?
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Answer: C — 91°
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Hint 1 of 2
Biggest + smallest = 180° − middle, so making that small means making the middle angle large.
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Hint 2 of 2
Push the middle angle as high as possible while keeping all three angles different whole numbers.
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Approach: maximise the middle angle
- The three angles add to 180°, so biggest + smallest = 180 − middle.
- To minimise that, maximise the middle angle: take 1°, 89°, 90° (all different, sum 180).
- Then biggest + smallest = 90 + 1 = 91°.
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