Doctor Rick discusses the concept of a pentagon, which has one complete turn at each corner, making a total of 360°. The sum of internal angles at these corners is the sum of the supplements, which are 180-A, 180-B, and X. A regular polygon, like the one in the center of a five-pointed star, has equal angles of 108 degrees each. The points of a golden five-pointed star are all 36 degrees each, making the other two angles of the star shape a regular pentagram.
Exterior angles of polygons are the angle between any side of a shape and a line extended from the next side. The exterior angle sum theorem states that the exterior angles of any shape are equal to the sum of the other interior angles. For example, a 5-pointed star has a 36° interior angle at each point (vertex), so the exterior angle at each point is 360°-36° = 324°.
The Exterior Angle Sum Theorem states that one exterior angle is equal to the sum of the other interior angles, which is very powerful. For example, the star pentagon can be calculated using the exterior angle theorem, where angle 1 = alpha1 + beta and angle 2 = alpha1 + theta. By the time you get back to where you started, you’ll have made exactly m full turns, so the sum of the exterior angles is 360m degrees.
In conclusion, the sum of exterior angles of a polygon is equal to 360°, and the sum of interion angles of a pentagram is also equal to 360°.
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