A pentagram is a polygon in the shape of a five-pointed star. Below are 2 different varieties of pentagrams.

You are watching: Angles of a 5 point star The pentagram is part of the national flags of numerous countries. The adhering to are a few examples. ## Regular pentagram

A regular pentagram consists of 5 congruent isosceles triangles creating the 5 points, and a regular pentagon in that is center. ## Irregular pentagrams

The triangles creating the 5 point out of an rarely often, rarely pentagram are not every congruent. It complies with that the pentagon in the facility of an rarely often, rarely pentagram is an rarely often, rarely pentagon. ## Construct a continuous pentagram

A constant pentagram can be built by illustration the 5 diagonals that a regular pentagon. Two unique diagonals can be drawn from any vertex that a regular pentagon. Drawing diagonals from every the vertices, as displayed in the continual pentagon above, develops a continuous pentagram.

You can also extend the sides of a consistent pentagon to type a pentagram. The 5 points of intersection created by expanding each side of the consistent pentagon displayed above kind the five points of a constant pentagram.

## Angle procedures of a continuous pentagram

The angles formed at each of the five points of a consistent pentagram have equal actions of 36°. For continuous pentagon ABCDE, presented above, each interior angle has actually a measure up of 108°. Angle BCD = 108°, therefore its supplement, angle HCD = 72°. Due to the fact that the five triangles forming pentagram FGHIJ space isosceles, their base angles space congruent, so angle HDC = 72°.

Also, the sum of the inner angles the a triangle is 180°, so angle H = 180° - (72° + 72°) = 36°. The exact same is true for angles F, G, and I, which likewise have procedures of 36°.

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## Symmetry in a continual pentagram

A regular pentagram has actually 5 currently of symmetry and also a rotational symmetry of stimulate 5, which method that it can be rotated in together a way that it will certainly look the very same as the original shape 5 time in 360°.