How To Calculate A Star’S Internal Angles?

Doctor Rick discusses the concept of a pentagon, where each corner makes exactly one complete turn in a circle. The sum of all the interior angles of five triangles is 5*180°=900°. To find the acute angle x in a 5-pointed regular star, three different methods are used.

The angle of each exterior point is always the sum of the two adjacent interior angles – 180°. This is because given internal angles A and B, the angles of the triangle are 180 – A, 180 – B, and X.

An interesting geometry question involving a pentagram or 5-pointed star is presented, which asks about the sum of corner angles in a regular 5-sided star. The internal angles of a regular polygon, such as a pentagon, can be found using the Exterior Angle Theorem. The sum of interior angles is equal to 180°*(n-2), where n is a number of angles, and each exterior angle is supplementary to its interior.

The exterior angle theorem states that one exterior angle is equal to the sum of the other interior angles, making it powerful for finding the sum of interior angles. For example, an (n/1) star is just a regular n-gon, and the sum of interior angles is equal to 180(n-2) as the sum of the degrees.

To solve the question, consider the regular pentagon formed inside this star and calculate the sum of the interior angles. Another way to think of it is when considering the angle angles in a hexagon.