1, a polygon has as many angles as there are sides. This is because each side of a polygon is adjacent to two corners. Therefore, a polygon with n sides will have 2n angles. It should be noted that the internal angle of the polygon is calculated here. If a polygon is convex, its inner angle will be less than 360 degrees.

2. There are several special polygons, such as triangles, squares and regular pentagons. These polygons all have specific angles and sides. For example, a regular triangle has three sides and three angles, a regular quadrilateral or square has four sides and four angles, and a regular pentagon has five sides and 10 angles.

3. Knowing the number of polygon angles can be applied to architectural design, graphic drawing, robot path planning and other fields. For example, in the field of architectural design, architects need to consider the shape, angle and spatial distribution of buildings in order to achieve a balance between functionality and aesthetics.

Characteristics of angles in mathematics

1, the size of the angle is a way to measure the included angle between two sides. In plane geometry, angles are usually measured in degrees, and a complete circle is defined as 360 degrees. The angle can also be measured in radians, where the ratio of the circumference to the radius of the circle defines the radius of the circle. In three-dimensional space, the angle can also be described by the angle between three-dimensional vectors.

2. The directionality of angle is also one of its important characteristics. In plane geometry, the direction of an angle is usually determined by the direction of a straight line determined by its two sides. In three-dimensional space, the direction of an angle is determined by its plane or spatial direction. Angles can be classified according to their shapes and types. For example, a right angle is an angle of 90 degrees, and all three angles in an equilateral triangle are angles of 60 degrees.

3. There are many important properties and theorems about angles in mathematics. For example, the addition and subtraction of angles can be used for geometric transformation and solving geometric problems. Trigonometric functions such as sine, cosine and tangent of an angle can be used for various mathematical calculations and solving practical problems.