Outside the pentagon II

A regular pentagon and two equilateral triangles. What’s the angle α?

Scroll down for a solution to this problem.


The angle α is 30°.

Solution by Marshall W. Buck.

By symmetry, the orange segments have the same length, so the green dotted circle, centered where the equilateral triangles meet, contains the three points defining the angle to be determined. But the arc is 60 degrees at the center, so it appears as 30 degrees from any point on the green dotted circle.


Please find here the video solution: Video: Outside the pentagon II.

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