10. Five identical right-angled triangles can be arranged so that their larger acute angles touch to form the star shown in the diagram. It is also possible to form a different star by arranging more of these triangles so that their smaller acute angles touch. How many triangles are needed to form the second star?
A 10 B 12 C 18 D 20 E 24
Official solution
SolUtion D
Since the five identical triangles meet at a point, the size of the larger acute angle in each triangle is 360∘÷5=72∘. Therefore the smaller acute angle in each triangle is 180∘−90∘−72∘=18∘. Hence, since the second star is formed using the triangles whose smaller acute angles touch, the number of triangles needed to form the second star is 360÷18=20.
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