Right angle is a very important concept in the area of mathematics, on the basis of right angle concept whole of advanced geometry is built (Trigonometry).

So whenever you are in need to calculate the heights of building or dealing with inclined planes we make use of Pythagorean right angled triangle.It consists of perpendicular distance, an inclined plane and a base.  

A right angle is an angle whose degree measure is 90º.
Right Angle

In the above diagram angle B is marked as 90º and hence it is a right angle. The box symbol ⌉ represents the right angle and indicates the angle measure is 90º. The two intersecting rays AB and BC are said to be perpendicular to each other.

In general lines that intersect to form right angles are perpendicular.
If the side CB is extended to CD, the angle formed ABD is also a right angle.
Right Angle on Both Sides
The supplementary angle of a right angle is also a right angle.

Indeed when two perpendicular lines intersect, they form four right angles around the point of intersection.

Four Right Angles

Unlike acute and obtuse angles all right angles are congruent as all of them measure 90º.
1.  Identify the right angles in the diagram given below:

Right Angle Example  

    The angle in the sketch marked with the right angle symbol ⌉ is ∠DOB.
    m ∠ EOC = m ∠ EOD +m ∠ DOC.                         Angle addition property.
                    = 30º + 60º = 90º.
    Thus two adjacent complementary angles form a right angle.
    Hence, the two right angles in the diagram are ∠DOB and ∠EOC.


2.  Right angle in polygons

     A triangle can have at most one right angle. A triangle with one of its angle as a right angle is called a right triangle.
    
     Example of Right Angle

     All the four angles of a rectangle or a triangle are right angles.

     Solving Right Angle Problem
    
    The diagonals bisect each other in right angles in a rhombus.

Right Angle Example Problems

   The diagonals of a square also bisect each other at right angles. as a square is also a special Rhombus.  


3. How many right angles do you find on the surface of a cube.

   Right Angle Problems

   Each vertex of the cube is the intersection of three square faces. Hence three right angles are formed around each vertex. You can identify the eight vertices of the cube marked as A, B, C, D........H. 

   Hence the number of right angles in a cube = 8 x 3 = 24.
1. The walls make right angles with the floor they meet.
2.  Your books and notebooks have rectangular surfaces.  Hence the adjacent sides of a book make a right angle.
     Indeed where ever you see a rectangular surface, you can identify a right angle there.
3.  The four angles formed in The Holy Cross are right angles.
    
     Right Angle Real Life

4.  Right triangle models many real life situations and the problems are solved using either Pythagorean theorem or trigonometric ratios. For example, an object erected vertically like a building makes a right angle with the horizontal. The North - South line are at right angles to the West - East line.

5. The coordinate axes, X and Y axes are perpendicular to each other. Thus the two axes form four right angles in the four quadrants as shown below.

     Axes

6. Boomerangs are flight toys that return to the thrower after moving a distance in the air. The angle between the wings vary from 70º to 140º.  But in traditionally designed Boomerangs the angle between the wings is fixed as a right angle.
   Right Angle Boomerang

   In general a right angle can be observed whenever two intersecting sides, arms or surfaces are perpendicular to each other.