Problem 26 · 2024 Math Kangaroo
Stretch
Geometry & Measurement
spatial-reasoning
Three angles \(\alpha\), \(\beta\) and \(\gamma\) are drawn on squared paper (see diagram). How big is \(\alpha + \beta + \gamma\)?
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Answer: E — another angle
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Hint 1 of 3
Each angle sits at a grid point, so its size is the arctangent of a simple rise-over-run fraction you can read off the squares.
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Hint 2 of 3
Find each angle as an arctangent, then add the three — do not assume the total is one of the round numbers offered.
Still stuck? Show hint 3 →
Hint 3 of 3
Compare your computed sum with the four listed values before settling on an answer.
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Approach: read each angle as an arctangent of a grid slope, then add
- Each of α, β, γ is the angle a drawn line makes with the grid, so each equals an arctangent of a small fraction read straight off the squares.
- Adding the three arctangent values gives a sum that is not 72°, 75°, 87.5° or 96°.
- Since the total matches none of the tidy listed values, the answer is another angle.
Mark:
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