Vertically Opposite Angles : 2

   When two lines intersect each other at a point, the vertically opposite angles are equal.All angles of vertically opposite angles add upto 180°. A straight line crosses two parallel lines:Corresponding angles are equal – we look for an F shape which may be upside down and/or back to front. 

          Let A lie between B and C on the line BC, and also between D and E on the line DE. Then BAD and CAE are called vertically opposite angles.vertically opposite angles are normally equal in measure.
The idea is to add the same supplementary angles to both, getting 180.

                                                         

In detail,

                               |BAD| + |BAE| = 180;
                              
                               |CAE| + |BAE| = 180;

                              so subtracting gives:

                               |BAD| - |CAE| = 0 ;

                               |BAD| = |CAE| :                                                                        

 

Vertically opposite angles:

 

General properties of Angles:

  • When two lines meet an angle is formed. A
  • Angles is calculated using protractor in degrees. 75 degrees is written 75°.
  • The total angle given out by the line AB when it is rotated until it comes back to its original position is 360°.
  • The angle that is less than 90° is called acute.
  • The angle which is exactly 90° is called a right angle and often denoted by a box. The lines are at perpendicular.
  • The angle of more than 90° but less than 180° is called obtuse.
  • The angle of more than 180° but less than 360° is called reflex.

 

Vertically opposite angles:

 

Example 1:

From the given vertically opposite angle shown below, Find angles a°, b° and c° ,

                                            

Because b° is vertically opposite 60°, it must also be 60°

A full circle is 360°, so that leaves 360° - 2×60° = 240°

Angles a° and c° are also vertically opposite, so must also be equal, which means they are 120° each.

Answer: a = 120°, b = 60° and c = 120°.