6.2.3 Polygon Angle Sums

Explanation
A decagon is a polygon with ten sides. To find the interior angle sum of a decagon, we can use the formula (n-2) * 180, where n is the number of sides. Plugging in 10 for n, we get (10-2) * 180 = 8 * 180 = 1440 degrees. Therefore, the correct answer is 1440 degrees.

Explanation
The interior angle sum of a polygon is given by the formula (n-2) * 180, where n is the number of sides of the polygon. In the case of a pentagon (a polygon with 5 sides), the formula becomes (5-2) * 180 = 3 * 180 = 540 degrees. Therefore, the correct answer is 540 degrees.

Explanation
An octagon has 8 sides. To find the interior angle sum of any polygon, we use the formula (n-2) * 180 degrees, where n is the number of sides. Substituting n=8, we get (8-2) * 180 = 6 * 180 = 1080 degrees. Therefore, the correct answer is 1080 degrees.

Explanation
Exterior angle sum of any polygon = 360

Explanation
The measure in degrees of one exterior angle of a regular octagon is 45. In a regular octagon, all the exterior angles are congruent, meaning they have the same measure. Since there are 8 exterior angles in an octagon and the sum of the exterior angles of any polygon is always 360 degrees, we can divide 360 by 8 to find the measure of each exterior angle. 360/8 = 45. Therefore, each exterior angle of a regular octagon measures 45 degrees.

Explanation
The measure in degrees of one exterior angle of a regular nonagon is 40. In a regular nonagon, there are nine equal exterior angles that add up to 360 degrees. Therefore, each exterior angle is 360 degrees divided by 9, which equals 40 degrees.

Explanation
A regular polygon is a polygon that has all sides of equal length and all angles of equal measure. The sum of the exterior angles of any polygon is always 360 degrees. Since each exterior angle measures 20 degrees, we can divide 360 by 20 to find the number of sides. 360/20 = 18. Therefore, a regular polygon with each exterior angle measuring 20 degrees has 18 sides.

Explanation
A regular polygon is a polygon with all sides and angles equal. The sum of the exterior angles of any polygon is always 360 degrees. If each exterior angle of a regular polygon measures 60 degrees, then there must be 6 sides in the polygon. This is because 360 divided by 60 equals 6. Therefore, the correct answer is 6.

Explanation
The measure of one interior angle of a regular pentagon is 108 degrees. A regular pentagon has five sides and five interior angles. To find the measure of one interior angle, we can use the formula (n-2) * 180 / n, where n is the number of sides of the polygon. Plugging in the values, we get (5-2) * 180 / 5 = 3 * 180 / 5 = 540 / 5 = 108. Therefore, the measure of one interior angle of a regular pentagon is 108 degrees.

Explanation
A regular decagon has 10 equal sides and 10 equal interior angles. To find the measure of one interior angle, we divide the sum of all interior angles (180 degrees) by the number of angles, which is 10. Therefore, each interior angle of a regular decagon measures 180/10 = 18 degrees.