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The interior angles of an equilateral triangle, square, regular pentagon are 60 °, 90 °, 108 ° respectively. The sum of the angles at a point is 360 °. So Î¸ = 360 - (60 + 90 + 108) = 102 °.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.