In a given decagon, all interior angles are equal to each other. Find its outer corner.

A polygon whose interior angles are equal to each other is called regular. The formula for finding one of the corners of a regular polygon: α = (180 ° * (n – 2)) / n, where α is the angle, n is the number of sides of the polygon.
Since the original polygon is a decagon, then n = 10. Substitute 10 into the formula.
α = (180 ° * (10 – 2)) / 10 = (180 ° * 8) / 10 = 144 °.
Then the value of the external angle at α is equal to 180 ° – 144 ° = 36 °.
Answer: 36 °.