Polygon, Pentagon And Decagon: Interior And Exterior Angle Sum! Trivia Quiz

Explanation
A nonagon is a polygon with nine sides. Therefore, the correct answer is 9.

Explanation
A regular polygon has congruent sides because all sides of a regular polygon are equal in length. It also has congruent angles because all angles of a regular polygon are equal in measure. However, a regular polygon does not have dents.

Explanation
The structure of The Pentagon has 5 sides. The Pentagon is a five-sided building located in Arlington, Virginia, and serves as the headquarters for the United States Department of Defense. It is named after its distinct shape, which resembles a regular pentagon.

Explanation
The figure shown in the question can be described as a regular polygon because all of its sides and angles are equal. It can also be described as a convex polygon because all of its interior angles are less than 180 degrees and all of its diagonals are contained within the shape. Lastly, it can be described as a hexagon because it has six sides. Therefore, the correct answer is I, II, and III.

Explanation
The interior angle sum of a polygon can be found by using the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, the polygon is a hexagon, which has 6 sides. Plugging in the value of n into the formula, we get (6-2) * 180 = 4 * 180 = 720. Therefore, the interior angle sum of a hexagon is 720 degrees.

Explanation
A convex polygon is a polygon in which all interior angles are less than 180 degrees. The sum of the interior angles of a convex polygon can be found using the formula (n-2) * 180, where n is the number of sides. In this case, the sum of the interior angles is given as 540 degrees. By rearranging the formula, we can solve for n: (n-2) * 180 = 540. Simplifying the equation, we get n - 2 = 3, which means n = 5. Therefore, a convex polygon with an interior angle sum of 540 degrees must have 5 sides.

Explanation
A regular dodecagon is a polygon with 12 sides, and each interior angle of a regular dodecagon can be found using the formula (n-2) * 180 / n, where n is the number of sides. Plugging in the value of n as 12, we get (12-2) * 180 / 12 = 150. Therefore, the measure of each interior angle of a regular dodecagon is 150 degrees.

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

Explanation
The exterior angle sum of any polygon is always 360 degrees. This means that if you add up all the exterior angles of a polygon, the total will always be 360 degrees. This is a property of polygons and is true for all polygons, regardless of the number of sides or the shape of the polygon.

Explanation
In a regular polygon, all exterior angles are equal. If one exterior angle is 20 degrees, then each exterior angle is 20 degrees. The sum of all exterior angles in any polygon is always 360 degrees. Therefore, the number of sides can be found by dividing 360 degrees by the measure of each exterior angle, which in this case is 20 degrees. 360/20 = 18. Hence, the polygon has 18 sides.

Explanation
The measure in degrees of each exterior angle of a regular decagon is 36. In a regular decagon, all the exterior angles are congruent, meaning they have the same measure. Since a decagon has 10 sides, the sum of all the exterior angles is 360 degrees. Therefore, each exterior angle of a regular decagon measures 360/10 = 36 degrees.