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.

Examples with solutions for Bisector

Exercise #1

Which of the following figures has a bisector?

Step-by-Step Solution

The answer is C because the angle bisector divides the angle into two equal angles. In diagram C, the angle bisector divides the right angle, which is equal to 90 degrees, into 2 angles that are equal to each other. $45=45$

Exercise #2

BD is a bisector.

What is the size of angle ABC?

Step-by-Step Solution

Since we are given that the value of angle DBC is 65 degrees, and we know that the angle bisector divides angle ABC into two equal angles, we can calculate the value of angle ABC:

$65+65=130$

130

Exercise #3

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

Step-by-Step Solution

Since an angle bisector divides the angle into two equal angles, and we are given that one angle is equal to 60 degrees. Angle $\alpha$ is also equal to 60 degrees

60

Exercise #4

ABCD is a square.

$∢\text{ABC}=\text{?}$

Step-by-Step Solution

Since in a square all angles are equal to 90 degrees, and BC bisects an angle, we can calculate angle ABC:

$90:2=45$

45

Exercise #5

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:

$20\times2=40$

30

Exercise #6

Given:

$∢\text{ABC}=90$

$∢DBC=45$

Is BD a bisector?

Yes

Exercise #7

$∢\text{ABD}=15$

BD bisects the angle.

Calculate the size of $∢\text{ABC}$.



30

Exercise #8

$∢ABC=120$

$∢ABD=60$

Which of the following are true?

Video Solution

BD bisects $∢ABC$.

Exercise #9

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

45

Exercise #10

$∢DBC=90°$

BE cross $∢\text{DBA}$

Find the value $\alpha$

45

Exercise #11

BO bisects $∢ABD$.

$∢\text{ABD}=85$

Calculate the size of

$\sphericalangle ABO\text{.}$

42.5

Exercise #12

$∢\text{ABD}=90$

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

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

Calculate the size of $∢ABC$.

45

Exercise #13

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

80

Exercise #14

$∢ABC\text{ }=130$

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

65

Exercise #15

a is a bisector.

$∢BAC = 80°$

Calculate angle $\alpha$.