Problem 20 · 2018 Math Kangaroo
Stretch
Geometry & Measurement
Two rectangles form angles of \(40^\circ\) and \(30^\circ\) respectively with a straight line, as shown. How big is angle \(\alpha\)?
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Answer: E — another value
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Hint 1 of 2
Work around the point where the two rectangles meet the line, using their right angles.
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Hint 2 of 2
Add up the known angles and see whether the result is one of the listed values.
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Approach: angle chase around the meeting point
- Each rectangle contributes a 90° corner, and the rectangles meet the straight line at 40° and 30°.
- Combining these around the junction gives α = 110°.
- Since 110° is not among the options A–D, the answer is another value.
Mark:
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