A pentagram is a polygon in the form of a five-pointed star. Below are two different species of pentagrams.

You are watching: Angles of a five pointed star The pentagram is component of the nationwide flags of many countries. The adhering to are a couple of examples. ## Regular pentagram

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

The triangles creating the 5 clues of an rarely often rare pentagram are not every congruent. It follows that the pentagon in the facility of an rarely often rare pentagram is an irregular pentagon. ## Construct a constant pentagram

A constant pentagram deserve to be created by drawing the 5 diagonals that a consistent pentagon. Two unique diagonals deserve to be drawn from any type of vertex of a constant pentagon. Illustration diagonals from every the vertices, as presented in the constant pentagon above, develops a constant pentagram.

You can likewise extend the sides of a regular pentagon to kind a pentagram. The five points of intersection created by extending each next of the consistent pentagon displayed above kind the five points the a continual pentagram.

## Angle measures of a consistent pentagram

The angles developed at every of the 5 points of a constant pentagram have actually equal procedures of 36°. For regular pentagon ABCDE, presented above, each inner angle has actually a measure of 108°. Edge BCD = 108°, for this reason its supplement, edge HCD = 72°. Since the 5 triangles forming pentagram FGHIJ space isosceles, your base angles room congruent, so angle HDC = 72°.

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

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## Symmetry in a consistent pentagram

A constant pentagram has 5 present of symmetry and also a rotational symmetry of order 5, which way that it deserve to be rotated in such a means that it will certainly look the exact same as the initial shape 5 time in 360°.