Geometry/Angles

An angle is the union of two rays with a common endpoint, called the vertex. The angles formed by vertical and horizontal lines are called right angles; lines, segments, or rays that intersect in right angles are said to be perpendicular. Angles, for our purposes, can be measured in either degrees (from 0 to 360) or radians (from 0 to ). Angles length can be determined by measuring along the arc they map out on a circle. In radians we consider the length of the arc of the circle mapped out by the angle. Since the circumference of a circle is , a right angle is radians. In degrees, the circle is 360 degrees, and so a right angle would be 90 degrees. Naming Conventions Angles are named in several ways. By naming the vertex of the angle (only if there is only one angle formed at that vertex; the name must be non-ambiguous) By naming a point on each side of the angle with the vertex in between. By placing a small number on the interior of the angle near the vertex. Classification of Angles by Degree Measure Acute Angle an angle is said to be acute if it measures between 0 and 90 degrees, exclusive. 150px|Acute Angle Right Angle an angle is said to be right if it measures 90 degrees. notice the small box placed in the corner of a right angle, unless the box is present it is not assumed the angle is 90 degrees. all right angles are congruent 100px Obtuse Angle an angle is said to be obtuse if it measures between 90 and 180 degrees, exclusive. 150px|Obtuse Angle Special Pairs of Angles adjacent angles adjacent angles are angles with a common vertex and a common side. adjacent angles have no interior points in common. complementary angles complementary angles are two angles whose sum is 90 degrees. complementary angles may or may not be adjacent. if two complementary angles are adjacent, then their exterior sides are perpendicular. supplementary angles two angles are said to be supplementary if their sum is 180 degrees. supplementary angles need not be adjacent. if supplementary angles are adjacent, then the sides they do not share form a line. linear pair if a pair of angles is both adjacent and supplementary, they are said to form a linear pair. vertical angles angles with a common vertex whose sides form opposite rays are called vertical angles. vertical angles are congruent.