# Bisector - Examples, Exercises and Solutions

A bisector is a line segment that passes through the vertex of an angle and divides it into two equal angles.

The bisector can appear in a triangle, parallelogram, rhombus and in other geometric figures.

For example, a bisector that passes through an angle of $120°$ degrees will create two angles of $60°$ degrees each.

## Practice Bisector

### Exercise #1

ABCD is a deltoid.

$∢DAC=\text{?}$

### Step-by-Step Solution

As we know that ABCD is a deltoid, and AC is the bisector of an angle and therefore:

$BAC=CAD=2X$

Now we focus on the triangle BAD and calculate the sum of the angles since we know that the sum of the angles in a triangle is 180 degrees:

$2X+2X+2X+60=180$

$6X+60=180$

$180-60=6X$

$120=6X$

We divide the two sections by 6:$\frac{120}{6}=\frac{6x}{6}$

$20=x$

Now we can calculate the angle DAC:

$20\times2=40$

40

### Exercise #2

Which of the following figures has a bisector?

### Exercise #3

BD is a bisector.

What is the size of angle ABC?

130

### Exercise #4

Calculate the size of angle $\alpha$ given that it is a bisector.

45

### Exercise #5

Calculate angle $\alpha$ given that it is a bisector.

60

### Exercise #1

Given:

$∢\text{ABC}=90$

$∢DBC=45$

Is BD a bisector?

Yes

### Exercise #2

$∢\text{ABD}=15$

BD bisects the angle.

Calculate the size of $∢\text{ABC}$.



30

### Exercise #3

$∢\text{ABD}=90$

CB bisects $\sphericalangle\text{ABD}$.

$\sphericalangle\text{CBD}=\alpha$

Calculate the size of $∢ABC$.

45

### Exercise #4

$∢ABC=120$

$∢ABD=60$

Which of the following are true?

### Video Solution

BD bisects $∢ABC$.

### Exercise #5

$∢DBC=90°$

BE cross $∢\text{DBA}$

Find the value $\alpha$

45

### Exercise #1

BO bisects $∢ABD$.

$∢\text{ABD}=85$

Calculate the size of

$\sphericalangle ABO\text{.}$

42.5

### Exercise #2

What is the size of angle ABC given that BD is a bisector?

80

### Exercise #3

$∢ABC\text{ }=130$

Given that a is a bisector, calculate angle $\alpha$.

65

### Exercise #4

a is a bisector.

$∢BAC = 80°$

Calculate angle $\alpha$.

40

### Exercise #5

The triangle ABC is shown below.

CD bisects C.

Angle C equals 122 degrees.

Calculate angle $∢\text{ACD}$.