UKMT - Intermediate Mathematical Challenge - 2023 - 15 | Exact Science

15

How many of the following polygons could exist?

A triangle with all three sides the same length, but three different interior angles.

A quadrilateral with all four sides the same length, but four different interior angles.

A pentagon with all five sides the same length, but five different interior angles.

A. only the pentagon

B. only the quadrilateral

C. the quadrilateral and the pentagon

D. all three

E. none of them

Answer

A. only the pentagon

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SOLUTIOn

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