What are vertical angles? GRE Math Fact

When two lines intersect, two pairs of angles are formed. The opposite angles in such an intersection are called vertical angles.

Vertical angles are always equal to each other.

In the above figure,   and   are vertical angles. Such that = . Similarly  and  are vertical angles such that = 

Let’s look at an example where this concept plays a role:

Example:

In the above figure, lines  ,  and  intersect at point O. If  =100º and  =30º, what is the measure of  ?

A) 30º

B) 50º

C) 80º

D) 100º

E) 150º

Solution:

Step 1: First draw the vertical angle  as shown in the following figure:

Since  and  are vertical angles,  =  = 30º

Step 2:  ,  and  are angles along the straight line  and therefore the sum of their measures should be equal to 180º

 = 180º

Since  = 100º and  = 30º,  

The correct answer is B