Question

How to calculate sum of the internal angles of a star?

Answer 1

Answer:

Step-by-step explanation:

Five Angles in a Star. In a regular pentagram (5-pointed star), the angle in each point is 36 degrees, so the angles in all five points sum to 180 degrees: What about an irregular pentagram, such as the following  Now the angles might be all different from each other; the situation is much more complicated

Answer 2

Step-by-step explanation:

The sum of the interior angles of a pentagon is always 540°.

The angle of each exterior point is always the sum of the two adjacent interior angles - 180°. We can say this since, given internal angles A and B, the angles of the triangle are 180 - A, 180 - B, X. By definition of angles of a triangle, X is equal to 180−(180−A)−(180−B)=A+B−180.

Each interior angle of the pentagon is used twice, and there are 5 points, so (2×540)−(5×180)=180