Primary Mathematics Challenge - 2022 - 24 | Exact Science

24

Penny is pretty pleased with the pattern she has produced by placing regular pentagons next to each other. Tristan points out that there are acute angles between the outer pentagons. What is the size of these acute angles?

Answer

36°

SOLUTIOn

Each interior angle of a regular pentagon is 108°. There are three pentagons which meet to create the acute angle which will be 360° - 3(108°) = 360° - 324°= 36°.

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