Problem 15 · 2018 Math Kangaroo
Medium
Geometry & Measurement
transformations
Valentin draws a zig-zag line inside a rectangle as shown in the diagram. For that he uses the angles 10°, 14°, 33° and 26°. How big is the angle \(\varphi\)?
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Answer: A — 11°
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Hint 1 of 2
The zig-zag bounces between the two parallel long sides of the rectangle.
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Hint 2 of 2
Going along the path, the slope angles add and subtract; combine the four given angles to get φ.
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Approach: add and subtract the alternating zig-zag angles
- For a zig-zag between two parallel lines, the marked angles alternate in sign as the path turns.
- Combining them gives φ = (33° + 14°) − (10° + 26°) = 47° − 36° = 11°.
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