Fifteen triangles and four gons have 53 angles. How many triangles and quadrangles are there?

A quadrangle has one more angle than a triangle. This means that there are at least three corners in each figure. Together these are:

3 * 15 = 45 angles.

Subtract 45 from 53 and get 9 angles (one additionally for each quadrangle). This means that in the number of 15 figures there are 9 quadrangles and 15 – 9 = 6 triangles.



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