## Tuesday, September 26, 2023

### A list of many types of Angles from Geometry

There are many types of angles in geometry. I previously made a very basic list of angle pairings on my technical blog. This was written from the perspective of sketching shapes. The previous article only scratched the surface. As such, I've been wanting to revisit this topic from more generic geometry-based perspective. As an ad interm step, I've complied this list of different types of angles (basic types or shapes), angle pairings (group or related), and angle positions. In the future, I'll use this list as the basis for some sort of content with visual examples.

Angle Name Alternate name Definition Concept
Acute n/a An angle that measures less than 90 degrees. basic type
Full Full Rotation An angle that measures exactly 360 degrees. basic type
Obtuse n/a An angle that measures more than 90 degrees but less than 180 degrees. basic type
Reflex n/a An angle that measures more than 180 degrees but less than 360 degrees. basic type
Right n/a An angle that measures exactly 90 degrees. basic type
Straight n/a An angle that measures exactly 180 degrees. basic type
Zero n/a The two rays of the angle make zero degrees inclination with respect to each other basic type
Adjacent n/a Two angles that share a common vertex and a common ray but do not overlap. group
Alternate n/a Pairs of angles formed when a transversal intersects two lines. They are on opposite sides of the transversal and are congruent. group
Alternate Exterior n/a Pairs of angles formed when a transversal intersects two lines. They are on opposite sides of the transversal and outside the pair of lines. group
Alternate Interior n/a Pairs of angles formed when a transversal intersects two lines. They are on opposite sides of the transversal and inside the pair of lines. group
Congruent n/a Angles that have the same measure. group
Consecutive Exterior n/a Pairs of angles formed when a transversal intersects two lines. They are on the same side of the transversal and outside the pair of lines. group
Consecutive Interior n/a Pairs of angles formed when a transversal intersects two lines. They are on the same side of the transversal and inside the pair of lines. group
Corresponding n/a Pairs of angles formed when a transversal intersects two lines. They are on the same side of the transversal and in corresponding positions. group
Non-adjacent Complementary n/a Either of two non-adjecent angles whose sum is 90 degrees. group
Non-adjacent Explementary Conjugate Either of two non-adjecent angles whose sum is 360 degrees. group
Non-adjacent Supplementary n/a Either of two non-adjacent angles whose sum is 180 degrees. group
Central n/a An angle whose vertex is at the center of a circle. position
Inscribed n/a An angle formed by two chords in a circle with its vertex on the circle. position
Related n/a A general term used for pairs of angles with a common vertex, which can include various angle relationships. position
Adjacent Complementary n/a Either of two adjecent angles whose sum is 90 degrees. related
Adjacent Explementary n/a Either of two adjecent angles whose sum is 360 degrees. related
Vertically Opposite Vertical A pair of non-adjacent angles formed by the intersection of two straight lines and are opposite to each other. They have equal measures and will never form a linear pair. related
Concave n/a An angle with some of its interior points outside the polygon it forms. shape
Convex n/a An angle with all its interior points inside the polygon it forms. shape
Dihedral n/a The angle between two intersecting planes. shape
Exterior n/a An angle formed by one side of a polygon and the extension of an adjacent side. shape
Exterior Right n/a An angle formed by an extended side of a polygon and an adjacent side at a right angle. shape
Interior n/a Angles formed within the boundary of a polygon. shape
Reflex Interior n/a An angle greater than 180 degrees within a polygon. shape
Spherical n/a An angle formed by two intersecting great circles on a sphere. shape

The last time I mentioned geometry on this blog was back in 2007. It's a story about how I solved an "impossible" geometry problem on a technicality.