Right angles measure 90 degrees and form square corners. They also create a special kind of triangle called a right triangle. These are useful for finding the height and length of unknown objects because of the unique relationship between the lengths of their sides as described by the Pythagorean Theorem, a^2 + b^2 = c^2. Four right angles form a rectangle or square. These shapes are really two right triangles put together.
Acute angles measure less than 90 degrees. All triangles have at least two acute angles. If all three are acute, mathematicians call the triangle scalene. If they are all acute and equal, they form an equilateral triangle. If only two are equal, they form an isosceles triangle. They can also influence how the sides opposite them are named. For example, in a right triangle, the sides opposite the acute angles are called the legs, while the side opposite the right angle is the hypotenuse.
An obtuse angle is more than 90 degrees but less than 180. Triangles may only have one obtuse angle, but circles may have up to three. A triangle that contains an obtuse angle is called an obtuse triangle. The side across from the obtuse angle is always the triangle's longest side.
Mathematicians call an angle that is exactly 180 degrees a straight angle, or a line. Angles that are more than 180 degrees but less than 360 degrees are reflex angles. These can only exist in a circle. In addition to the basic types of angles, mathematicians also have names for angles that have special relationships with each other. For example, two angles that equal 90 degrees are called complementary angles. If they add up to 180 degrees, they are supplementary.