Geometric Angle Properties, Parallel Lines, and Polygon Angle Theorems

Acute angle

An angle that measures greater than 0∘0∘ and less than 90∘90∘.

Right angle

An angle that measures exactly 90∘90∘and is formed by two perpendicular lines.

Obtuse angle

An angle that measures greater than 90∘90∘ and less than 180∘180∘.

Straight angle

An angle that measures exactly 180∘180∘.

Reflex angle

An angle that measures greater than 180∘180∘ and less than 360∘360∘.

Angles on a straight line

Adjacent angles along a single straight line that add up to 180∘180∘.

Vertically opposite angles

Pairs of opposite angles formed by intersecting lines, which are always equal.

Angles at a point

The complete set of angles sharing a single vertex, which sum to 360∘360∘.

Triangle angle sum

The interior angles of any three-sided polygon always add up to 180∘180∘.

Corresponding angles

Angles situated in matching positions at each intersection where a transversal crosses parallel lines, which are equal.

Alternate angles

Angles located on opposite sides of a transversal between parallel lines, which are equal.

Co-interior angles

Angles situated between parallel lines on the same side of a transversal, which are supplementary and sum to 180∘180∘.

Exterior angle of a polygon

An angle formed on the outside of a shape by extending one of its sides.

Sum of exterior angles of a polygon

The constant sum of exterior angles for any convex polygon, which is always 360∘360∘.

Sum of interior angles of an polygon

The total measure of inside angles in a polygon with n sides, given by the formula