Geometry: Classifying Angles
This is a free lesson from our course in Geometry
 
   
This lesson explains about Classifying Angles. It will be done by the instructor presenting in own handwriting, using video and with the help of several examples with solution. Learning and developing skills in classifying angles, will help you later in classifying various geometric shapes like- triangles, quadrilaterals etc.
You may recall from earlier learning that an angle is a set of points that is the union of two rays having the same end points. It is represented by
The common endpoint of the two rays is the vertex of the angle. The two rays forming the angle are also called the sides of the angle. Then the amount through which one ray must be rotated around the vertex to bring it to the position of the other ray is called the magnitude of an angle. E.g. actually there are 360 degrees in a full circle. (More text below video...)
<h2> Geometry - Classifying Angles </h2> <p> point, degree, angle, measure, endpoint, ray, video, acute, right, straight, obtuse, vertex, adjacent, complementary, supplementary, solution, geometry help, linear pair, geometry tutorials, quizzes</p> <p> The classification of angles i.e. acute angle, right angle, obtuse angle, interior angle, straight angles and adjacent angles etc.</p>
Other useful lessons:
Point, Line, and Plane
Line Segment, Ray, Parallel Lines, Pependicular Lines
Midpoint and Congruence
(Continued from above) In broad sense the classification can be -Interior and Exterior angles. As the name suggests the interior parts that lie inside the angle are called interior angles and the part or the point that lies outside the angle is called exterior angle. Further on, there are different types of angle like - acute angle, obtuse angle, straight angle, right angle, complementary angle, supplementary angle and reflex angle etc. You'll also become familiar with the basics of the linear pairs of angles.
Acute angle: It is an angle, which measures more than 0 degree but less than 90 degrees. An acute angle is always lesser than right angle and straight angle.
Obtuse angle: It is an angle, which measures more than 90 degree but less than 180 degrees. Therefore, an obtuse angle is always greater than a right angle but less than a straight angle.
Right angle: It is an angle, which measures exactly 90 degrees i.e. exactly the half of a straight angle. It is the most common form of an angle; the best examples for a right angle can be the edges of the rectangular picture frames. A straight angle is formed when two rays starting from the same initial point travels and settles in a exact opposite direction. The measurement of a straight angle is 180 degree. You can say that a straight angle is more like half a circle.

Supplementary and complementary angles:

When the values of two angles add up to 180 degrees they are called supplementary angles. In this case, both the angles measure 90 degrees each so they sum up to 180 degrees. Supplementary angles need not touch each other or have to be in the same plane. The main criteria to fulfill are that the addition of their values should give 180 degrees. Then two angles are said to be complementary if they add up to 90 degrees. E.g. if there are two angles; Angle A measuring 30 degrees and B measuring 60 degrees, they add up to 90 degrees. These can be said to be complementary angles. An angle that measures more than 180 degrees but less than 360 degrees is called a reflex angle. A reflex angle is always lesser than a complete angle, which measures exactly 360 degrees. Two angles are called adjacent angles, if they have a common side and a common vertex.
The illustrative figures are given below:
Remember:
an acute angle is less than 90
a reflex angle is more than 180
an obtuse angle is more than 90
a straight angle is exactly 180
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