Right angle


The right angle is one formed by two lines perpendicular to each other, one being vertical and the other horizontal. Thus, its measure is 90º or π / 2 radians.

Seen in another way, when one line is on top of another and two equal adjacent angles are formed that add up to a straight angle (180º), each of these contiguous angles is right.In a similar way the Greek mathematician Euclid explains it.

It should also be noted that a right angle is equal to a perigonal or complete angle (360º) divided into four equal parts.

The right angle is usually represented by a square, as in the example above. This, unlike the other types of angles that are represented as arcs or semicircles.

In practice, it is relatively easy to find right angles around us. Let's think about the wall of our room that with the floor forms a right angle. Similarly, we can find 90º angles in the corners of a square window.

For more classifications, you can check our angle types article.

The right angle serves as a reference for various geometric figures, as we will see below.

Right angle examples

Some examples of right angles are:

  • Right triangle: One of its interior angles is right and, therefore, the other two must add up to 90º. This, because the interior angles of any triangle must add up to 180º.

In this type of figure, the well-known Pythagorean theorem is fulfilled, which tells us that the sum of each of the two legs squared is equal to the hypotenuse squared. This, being the legs the sides of the figure that form the right angle, while the hypotenuse is the side that is in front of the right angle.

So, looking at the figure above, the Pythagorean theorem dictates the following:

AC2 = AB2 + BC2

  • Square and rectangle: In a square and in a rectangle it is true that all interior angles are equal to 90º.
  • Rhombus: When the diagonals of a rhombus cross, four right angles are formed (the same happens with the diagonals the square).

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