In the center is a 5-sided regular polygon (a regular
pentagon). The sum of the interior angles of a polygon
is gotten by the formula:
SUM OF INTERIOR ANGLES = (NUMBER OF SIDES - 2) * 180°
For a 5-sided polygon (pentagon) this is (5-2)*180° = 3*180°=540°
Since all 5 angles of a regular pentagon are equal, each
interior angle of the regular pentagon is 540/5=108
Its suppplement is found by subtracting 180°-108°=72°.
We'll mark it 72°:
That 72° angle is one of the base angles of an isosceles
triangle. So we'll mark the other base angle 72° also.
Now we can find the angle at the top point of the star by
adding the two equal base angles and subtracting from 180°.
72° + 72° = 144°
180° - 144° = 36°
So each point of the star is 36°