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Types of Angles

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Types of 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 2π). 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 2π, 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.vertical angles are congruent.

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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

Obtuse Angle:-an angle is said to be obtuse if it measures between 90 and 180 degrees, exclusive.

Special Pairs of Angles

adjacent anglesadjacent angles are angles with a common vertex and a common side.adjacent angles have no interior points in common.

complementary anglescomplementary 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 anglestwo 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 pairif a pair of angles is both adjacent and supplementary, they are said to form a linear pair.

vertical anglesangles with a common vertex whose sides form opposite rays are called vertical angles.

Vertical angles are a pair of angles with a common vertex whose sides form opposite rays. An extensively useful fact about vertical angles is that they are congruent. Aside from saying that any pair of vertical angles "obviously" have the same measure by inspection, we can prove this fact with some simple algebra and an observation about supplementary angles. Let two lines intersect at a point, and angles A1 and A2 be a pair of vertical angles thus formed. At the point of intersection, two other angles are also formed, and we'll call either one of them B1 without loss of generality. Since B1 and A1 are supplementary, we can say that the measure of B1 plus the measure of A1 is 180. Similarly.

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