The three corners of a convex polygon are 120 degrees, and the rest are 160 degrees.
| May 24, 2021 | education
The three corners of a convex polygon are 120 degrees, and the rest are 160 degrees. Find the number of sides of the polygon.
We denote the number of angles of the polygon through n, then by the formula for the sum of the angles of the polyhedron:
180 * (n – 2) = 3 * 120 + (n – 3) * 160.
Where (n – 3) is the number of corners minus 3 corners of 120 each.
180 * n – 360 = 360 + 160 * n – 480.
180 * n – 160 * n = 720 – 480.
20 * n = 240.
n = 240/20 = 12.
Answer: A polygon has 12 sides.
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