Problem 19 · 2021 Math Kangaroo
Stretch
Geometry & Measurement
symmetry
What is the sum of the six marked angles in the picture?
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Answer: C — 1080°
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Hint 1 of 2
Don't try to measure any single angle — look for whole triangles in the mountain outline, since each triangle contributes a fixed \(180°\).
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Hint 2 of 2
The six marked corners are exactly the corners of a few triangles in the figure; add up those triangles' angle sums.
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Approach: bundle the marked corners into whole-triangle angle sums
- Each marked angle sits at a corner of the zig-zag mountain outline, and those corners are the vertices of the triangles the outline cuts the picture into.
- Instead of finding any one angle, group the six marked corners so that together they form six triangle-corner triples, each triple summing to \(180°\) (the straight pieces of the outline cancel out).
- Six such triangle angle sums give \(6\times 180° = 1080°\).
- So the six marked angles total \(1080°\), choice (C).
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