What is “Angle Bisector”? GRE Math Fact

Bisector is a term you may encounter in GRE geometry problems. So what the heck is a bisector and how do you use conquer bisector problems on the GRE?

Bisection is the division of something into two equal or congruent parts, usually by a line or a ray, which is then called a bisector. When a bisector, bisects an angle, it divides the angle into two equal parts. In the following figure,  is bisected by  such that  or in other words the angles are equal.  is also referred as the angle bisector of .

GRE problems can become somewhat more complicated when the ray divided an angle into a specific ratio. In such cases you need to apply little bit of algebra to the underlying geometry concept.

Let’s look at an example problem so that this concept is clear in your mind:

Example:

In the above figure,  splits the angle  in such a way that the measure of angle  and   are in the ratio 2:3. What is the measure of angle ?

A) 18

B) 20

C) 36

D) 45

E) 54

F) 60

Solution:

Step 1: We know that the sum of the interior angles is equal to the exterior angle. Therefore

From the figure we see that angle  is a right angle. It follows that

Step 2: Since the measure of angle and   are in the ratio 2:3, we can write  and 

Step 3: Since 

C is the correct answer.