# How many sides does a convex polygon have with each outside angle of 1 degree?

July 25, 2021 | education

| Since each outer corner of a convex polygon is 1 °, each inner corner of a convex polygon is 180 ° – 1 ° = 179 ° (since the inner and outer corners of a polygon are adjacent, and the sum of adjacent angles is 180 °).

The sum of the angles of a convex polygon is calculated by the formula:

S = 180 ° * (n – 2),

where n is the number of sides of the convex polygon.

Since all angles of a convex polygon are 179 ° each, the sum of all angles will be 179 ° * n.

Thus:

180 ° * (n – 2) = 179 ° * n;

180 ° * n – 180 ° * 2 = 179 ° * n;

180 ° * n – 360 ° = 179 ° * n;

180 ° * n – 179 ° * n = 360 °;

1 ° * n = 360 °;

n = 360 ° / 1 ° (proportional);

n = 360.

Answer: A convex polygon with each external angle of 1 ° has 360 sides.

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