Problem 14 · 2012 Math Kangaroo
Medium
Geometry & Measurement
The diagram shows a five-pointed star. How big is the angle A?
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Answer: C — 51°
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Hint 1 of 2
Outer angles of the star sit on triangles — use the exterior-angle idea.
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Hint 2 of 2
Combine the marked 100°, 93° and 58° through the little triangles to reach the angle A.
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Approach: exterior-angle chasing
- At the crossing points, an exterior angle of a small triangle equals the sum of the two remote interior angles.
- Chasing the marked angles 100°, 93° and 58° through the overlapping triangles gives angle A = 93° − (100° − 58°).
- So A = 93° − 42° = 51°.
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