Angle - Types of Angles

Types of Angles

• An angle equal to 1/4 turn (90° or π/2 radians) is called a right angle.

  Two lines that form a right angle are said to be perpendicular or orthogonal.

• Angles equal to 1/2 turn (180° or two right angles) are called straight angles.
• Angles equal to 1 turn (360° or four right angles) are called full angles.
• Angles that are not right angles or a multiple of a right angle are called oblique angles.
• Angles smaller than a right angle (less than 90°) are called acute angles ("acute" meaning "sharp").
• Angles larger than a right angle and smaller than a straight angle (between 90° and 180°) are called obtuse angles ("obtuse" meaning "blunt").
• Angles larger than a straight angle but less than 1 turn (between 180° and 360°) are called reflex angles.
• Angles that have the same measure (i.e. the same magnitude) are said to be equal (UK) or congruent (USA). An angle is defined by its measure and is not dependent upon the lengths of the sides of the angle (e.g. all right angles are congruent).
• Two angles opposite each other, formed by two intersecting straight lines that form an "X"-like shape, are called vertical angles or opposite angles or vertically opposite angles. These angles are equal in measure.
• Angles that share a common vertex and edge but do not share any interior points are called adjacent angles.
• Two angles that sum to one right angle (90°) are called complementary angles.

  The difference between an angle and a right angle is termed the complement of the angle.

• Two angles that sum to a straight angle (180°) are called supplementary angles.

  The difference between an angle and a straight angle (180°) is termed the supplement of the angle.

• Two angles that sum to one turn (360°) are called explementary angles or conjugate angles.
• An angle that is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A concave simple polygon has at least one interior angle that exceeds 180°.

  In Euclidean geometry, the measures of the interior angles of a triangle add up to π radians, or 180°, or 1/2 turn; the measures of the interior angles of a simple quadrilateral add up to 2π radians, or 360°, or 1 turn. In general, the measures of the interior angles of a simple polygon with n sides add up to radians, or °, or (2n − 4) right angles, or (n/2 − 1) turn.

• The angle supplementary to the interior angle is called the exterior angle. It measures the amount of rotation one has to make at this vertex to trace out the polygon. If the corresponding interior angle is a reflex angle, the exterior angle should be considered negative. Even in a non-simple polygon it may be possible to define the exterior angle, but one will have to pick an orientation of the plane (or surface) to decide the sign of the exterior angle measure.

  In Euclidean geometry, the sum of the exterior angles of a simple polygon will be one full turn (360°).

• Some authors use the name exterior angle of a simple polygon to simply mean the explementary (not supplementary!) of the interior angle. This conflicts with the above usage.
• The angle between two planes (such as two adjacent faces of a polyhedron) is called a dihedral angle. It may be defined as the acute angle between two lines normal to the planes.
• The angle between a plane and an intersecting straight line is equal to ninety degrees minus the angle between the intersecting line and the line that goes through the point of intersection and is normal to the plane.
• Alternate angles, corresponding angle, interior angles and exterior angles are associated with a transversal of a pair of lines by a third.
• A reference angle is the acute version of any angle determined by repeatedly subtracting or adding 180 degrees, and subtracting the result from 180 degrees if necessary, until a value between 0 degrees and 90 degrees is obtained. For example, an angle of 30 degrees has a reference angle of 30 degrees, and an angle of 150 degrees also has a reference angle of 30 degrees (180-150). An angle of 750 degrees has a reference angle of 30 degrees (750-720).