Problem 23 · 2025 Math Kangaroo
Stretch
Spatial & Visual Reasoning
transformations
Louise places three rectangular pictures as shown in the figure. What is the size of the angle α?
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Answer: B — 70°
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Hint 1 of 2
Each picture is a rectangle, so every corner of it is a right angle (90°) — that is the key fact to lean on.
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Hint 2 of 2
Use a right-angle corner together with the marked 62° to find a small leftover angle, then combine it with the 42°.
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Approach: angle-chase using the rectangles' right angles
- Because each picture is a rectangle, the corner sitting at the 62° mark is a right angle, so beyond the 62° there is \(90^\circ-62^\circ=28^\circ\) left over.
- That 28° lines up next to the 42° gap, so \(\alpha=42^\circ+28^\circ\).
- Hence \(\alpha=70^\circ\), which is (B).
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