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 |
Adjacent Supplementary |
Linear Pair |
Either of two adjecent supplementary angles. |
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.