Note that it is not added to n, but to (n- 1). For example, * * * has eight rays, so there are angles: 1+2+3+4+5+6+7 = 28 angles.
In the case of multiple vertices, that is, polygons (such as triangles), you only need to count the angles of each vertex of the polygon according to the above method, and then add up the angles of each vertex of the polygon to get the total number of angles.
How to calculate the angle number:
(1) How many angles?
As can be seen from the textbook, the angles mentioned are generally less than 180 degrees. Therefore, the number of angles should be less than 180 degrees.
(2) Calculation method
How many * * * angles can n rays from the end point O form (the maximum included angle is less than 180 degrees)? Because it is clear that each ray can form an angle with other (n- 1) rays, n rays can form n × (n- 1) angles.
But each angle is counted twice (for example, ∠AOB, once when considering ray OA and once when considering ray OB, but not two different angles, only one angle can be counted), so the actual number of different angles is: n× (n- 1) ÷ 2, which is a * *.