What is a right angle, acute angle, and obtuse angle?

1 Answer
Dec 28, 2015

Right angle is half of straight angle.
Acute angle has a smaller measure than right one, while obtuse angle has a bigger measure than right one.
See below for details.


We should start with a concept of an angle.
An angle is a geometric object formed by two half-lines (rays) with a common endpoint called vertex.

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Strictly speaking, there are two angles formed this way: from Ray1 to Ray2 clockwise and counterclockwise.

If Ray1 and Ray2 coincide, the angle between them is called full since it takes a full circle to move Ray1 to Ray2.
The measure of a full angle is, by definition, equal to #360^o#.
Obviously, angles measured at #0^o#, #720^o# etc. look exactly the same as an angle of #360^o#, that is Ray1 and Ray2 coincide.

In this terminology, if Ray1 and Ray2 are located along the same line but directed opposite to each other, they form half of a full angle, this angle is called straight and is measured at #180^o#.

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Half of a straight angle would be formed by perpendicular to each other Ray1 and Ray2. This is the right angle, and its measure in degrees is #90^o#.
Acute angles are smaller than right ones and obtuse angles are bigger.

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