Question

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

Answer 1

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.

Explanation:

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.

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`.

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.