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...)
(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°
Winpossible's online math courses and tutorials have gained rapidly popularity since
their launch in 2008. Over 100,000 students have benefited from Winpossible's courses...
these courses in conjunction with free unlimited homework help serve as a very effective
mathtutor for our students.

All of the Winpossible math tutorials have been designed by topnotch instructors
and offer a comprehensive and rigorous math review of that topic.

We guarantee that any student who studies with Winpossible, will get a firm grasp
of the associated problemsolving techniques. Each course has our instructors providing
stepbystep solutions to a wide variety of problems, completely demystifying the
problemsolving process!

Winpossible courses have been used by students for help with homework and by homeschoolers.

Several teachers use Winpossible courses at schools as a supplement for inclass
instruction. They also use our course structure to develop course worksheets.