Properties of Regular and Irregular Polygon

What is the main difference between regular and irregular polygons?

• Irregular polygons have all sides and angles equal.

• Regular polygons have all sides and angles equal, while irregular polygons have sides and angles of different lengths and measures.

• Regular polygons have all sides equal but not angles.

• Regular polygons have sides and angles of different lengths and measures.

Answer explanation

Regular polygons have all sides and angles equal, while irregular polygons have sides and angles of different lengths and measures.

Describe the properties of a polygon with 5 sides.

• A polygon with 5 sides is called a hexagon.

• A polygon with 5 sides is called a triangle.

• A polygon with 5 sides is called a circle.

• A polygon with 5 sides is called a pentagon.

Answer explanation

A polygon with 5 sides is called a pentagon.

Calculate the interior angles of a regular hexagon.

• 90 degrees

• 100 degrees

• 120 degrees

• 150 degrees

Answer explanation

The interior angles of a regular hexagon are calculated by dividing 360 degrees by the number of sides, resulting in 120 degrees for each angle.

Identify the number of sides in a polygon with interior angles of 135 degrees.

• 12

• 9

• 6

• 10

Answer explanation

A polygon with interior angles of 135 degrees has 9 sides. The formula to find the number of sides in a polygon is (n-2)*180 = total interior angles. Therefore, (n-2)*180 = 135, solving for n gives n=9.

What are the measurements of angles in a regular octagon?

• 90 degrees

• 150 degrees

• 120 degrees

• 135 degrees

Answer explanation

In a regular octagon, each interior angle measures 135 degrees. This is because the sum of all interior angles in an octagon is 1080 degrees, and when divided by 8 (number of angles), each angle measures 135 degrees.

Compare the measurements of sides in a regular hexagon and an irregular hexagon.

• The measurements of sides in a regular hexagon are different, while in an irregular hexagon, the measurements of sides are the same.

• Both regular and irregular hexagons have equal side measurements.

• Regular hexagons have varying side measurements, unlike irregular hexagons.

• The measurements of sides in a regular hexagon are equal, while in an irregular hexagon, the measurements of sides can vary.

Answer explanation

The measurements of sides in a regular hexagon are equal, while in an irregular hexagon, the measurements of sides can vary.

Calculate the interior angles of a regular decagon.

• 120 degrees

• 160 degrees

• 135 degrees

• 144 degrees

Answer explanation

The interior angles of a regular decagon can be calculated using the formula: (n-2) * 180 / n, where n is the number of sides. For a decagon (10 sides), the interior angle is (10-2) * 180 / 10 = 144 degrees.

Identify the number of sides in a polygon with interior angles of 120 degrees.

• 8

• 6

• 3

• 5

Answer explanation

A polygon with interior angles of 120 degrees must be a pentagon, which has 5 sides. Therefore, the correct number of sides is 5.

Compare the measurements of angles in a regular pentagon and an irregular pentagon.

• In a regular pentagon, all interior angles are 90 degrees, while in an irregular pentagon, the measurements of angles are fixed.

• Regular and irregular pentagons have the same angle measurements.

• The sum of interior angles in a regular pentagon is 360 degrees, while in an irregular pentagon, it is 540 degrees.

• In a regular pentagon, all interior angles are 108 degrees, while in an irregular pentagon, the measurements of angles can vary.

Answer explanation

In a regular pentagon, all interior angles are 108 degrees, while in an irregular pentagon, the measurements of angles can vary.

Determine if a polygon with 10 sides is regular or irregular.

• Regular

• Equilateral

• Symmetrical

• Irregular

Answer explanation

A polygon with 10 sides is irregular because a regular polygon must have all sides and angles equal, which is not the case for a 10-sided polygon.