What is the sum of the measures of the exterior angles of a decagon?
Polygons are closed two-dimensional figures with three or more straight lines. The name of a polygon is given depending on the number of sides it has. For example, an 8-sided polygon is called an octagon, while a 10-sided polygon is called a decagon.
Answer: The sum of the exterior angles of a decagon is 360°.
Let's understand the solution in detail.
A 10-sided polygon is called a decagon.
The sum of the exterior angles in an any polygon = 360°
Let us confirm it with a proof. A decagon has 10 sides, thus, its interior angles sum up to (n - 2) 180, where n = 10. So, substituting the value of 'n' in the formula:
Sum of interior angles of a polygon= (n - 2)180 = (10 - 2)180 = 8 ×180 = 1440°.
This means each interior angle of a decagon is 144° because 1440 ÷ 10 = 144. Since each exterior angle and interior angle form a linear pair, one exterior angle of a decagon = 180 - 144 = 36°. We know that a decagon had 10 exterior angles, so, 10 × 36 = 360°.
Hence, it is seen that the sum of the exterior angles of a decagon is 360°.
Therefore, the sum of the exterior angles of a decagon is 360°.