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 =100Âº and =30Âº, what is the measure of ?

A) 30Âº

B) 50Âº

C) 80Âº

D) 100Âº

E) 150Âº

Solution:

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

Since and are vertical angles, = = 30Âº

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

= 180Âº

Since = 100Âº and = 30Âº,

**The correct answer is B**

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