Calculate angle $$ \alpha $$ given that it is a bisector. α α α 60 60 60 A A A a a a

It is not possible to calculate.

BD is a bisector. What is the size of angle ABC? 65 65 65 A A A B B B C C C D D D

It is not possible to calculate.

$$ ∢ABC=120 $$ $$ ∢ABD=60 $$ Which of the following are true? A A A B B B C C C D D D 60 120

AB bisects $$ ∢\text{DBC} $$.

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

It is not possible to calculate.

Angle Bisector Practice Problems & Worksheets - Geometry

Master angle bisectors with step-by-step practice problems. Learn to identify, draw, and calculate bisectors in triangles, squares, and other geometric shapes.

📚What You'll Practice: Angle Bisector Skills

Identify angle bisectors in equilateral triangles and calculate equal angle measures
Draw bisectors in squares and rhombuses to divide 90° angles into equal parts
Apply angle bisector properties in parallel line configurations and circle geometry
Solve problems involving bisectors creating 30°, 45°, and other specific angle measures
Determine relationships between bisectors and geometric shape properties
Calculate unknown angles when bisectors divide original angles into equal parts

Understanding Bisector

Complete explanation with examples

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.

Detailed explanation

Practice Bisector

Test your knowledge with 7 quizzes

The triangle ABC is shown below.

CD bisects C.

Angle C equals 122 degrees.

Calculate angle $∢\text{ACD}$ .

Examples with solutions for Bisector

Step-by-step solutions included

Exercise #1

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

Answer:

Video Solution

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:

$65+65=130$

Answer:

130

Video Solution

Exercise #3

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. $45=45$

Answer:

Video Solution

Exercise #4

ABCD is a square.

$∢\text{ABC}=\text{?}$

Step-by-Step Solution

Due to the fact that all angles in a square are equal to 90 degrees, and BC bisects an angle, we can calculate angle ABC accordingly:

$90:2=45$

Answer:

Video Solution

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:

$20\times2=40$

Answer:

Video Solution

Frequently Asked Questions

Everything you need to know about Bisector

What is an angle bisector and how do you identify one?

An angle bisector is a line segment that passes through the vertex of an angle and divides it into two equal angles. You can identify a bisector by checking if it creates two angles of equal measure from the original angle.

How do you find the measure of angles created by a bisector?

To find the measure of angles created by a bisector, divide the original angle by 2. For example, if a bisector divides a 120° angle, each resulting angle measures 60°.

What are the angle measures when a bisector divides angles in an equilateral triangle?

In an equilateral triangle, each interior angle measures 60°. When divided by a bisector, each resulting angle measures 30°, since 60° ÷ 2 = 30°.

How many angle bisectors does a triangle have?

A triangle has exactly three angle bisectors, one for each of its three interior angles. Each bisector starts at a vertex and divides that vertex's angle into two equal parts.

What happens when you draw a bisector in a square?

When you draw a bisector in a square (where each angle is 90°), it divides the right angle into two 45° angles. This creates two congruent right triangles within the square.

Can angle bisectors be parallel to each other?

Yes, angle bisectors can be parallel when they bisect corresponding angles formed by parallel lines and a transversal. If the original corresponding angles are equal, their bisectors will also be parallel.

How do you draw an angle bisector step by step?

1. Place the compass point on the vertex of the angle. 2. Draw an arc that intersects both sides of the angle. 3. Place the compass on each intersection point and draw intersecting arcs. 4. Draw a line from the vertex through the intersection of the arcs.

What is the relationship between angle bisectors and perpendicular lines?

When two lines intersect perpendicularly (forming 90° angles), their angle bisectors divide each right angle into two 45° angles. The bisectors themselves are also perpendicular to each other.

Continue Your Math Journey

Master Bisector first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Sides, Vertices, and Angles Types of Angles Sum and Difference of Angles Sum of Angles in a Polygon The Sum of the Interior Angles of a Triangle Exterior angles of a triangle

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Angle Bisector Practice Problems & Worksheets - Geometry

Understanding Bisector

Practice Bisector

Examples with solutions for Bisector

Frequently Asked Questions

What is an angle bisector and how do you identify one?

How do you find the measure of angles created by a bisector?

What are the angle measures when a bisector divides angles in an equilateral triangle?

How many angle bisectors does a triangle have?

What happens when you draw a bisector in a square?

Can angle bisectors be parallel to each other?

How do you draw an angle bisector step by step?

What is the relationship between angle bisectors and perpendicular lines?

Continue Your Math Journey

Suggested Topics to Practice in Advance

Topics Learned in Later Sections

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