Practice Triangles in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A polygon with exactly three sides and three interior angles that always sum to exactly 180 degrees.

The simplest polygon—you need at least 3 sides to enclose space.

Showing a random 20 of 50 problems.

Example 1

challenge

How many non-congruent triangles have integer side lengths and a perimeter of

12

Example 2

hard

Triangle

ABC

has

\angle A = 40^\circ

and the bisector of

\angle B

meets

AC

D

so that

\angle BDA = 100^\circ

. Find

\angle C

Example 3

easy

Two angles of a triangle are

50^\circ

and

60^\circ

. Find the third angle.

Find the third angle x.

Example 4

medium

In a triangle, the longest side is opposite which angle?

Example 5

easy

True or false: a triangle can have one obtuse angle and one right angle.

Example 6

medium

A triangle has angles

x

x + 10^\circ

, and

x + 20^\circ

. Is the triangle acute, right, or obtuse?

All angles acute: 50°, 60°, 70°.

Example 7

easy

Can a triangle have two right angles?

Example 8

easy

An isosceles triangle has a vertex angle of

40^\circ

. Find each base angle.

Find each base angle x in this isosceles triangle.

Example 9

medium

In a right triangle, one acute angle is twice the other. Find both acute angles.

One acute angle (60°) is twice the other (30°).

Example 10

easy

One angle of a triangle is

90^\circ

. What type is it (by angles)?

Example 11

medium

An exterior angle of a triangle is

130^\circ

. What is the sum of the two non-adjacent interior angles?

Example 12

medium

The three angles of a triangle are in the ratio

2:3:4

. Find the measure of each angle.

Angles in ratio 2:3:4 are 40°, 60°, and 80°.

Example 13

challenge

In triangle

ABC

\angle B = 50^\circ

and

\angle C = 30^\circ

. Point

D

lies on side

BC

such that

AD = BD

. Find

\angle DAC

Example 14

medium

In a triangle, the largest angle is opposite the longest side. If a triangle has sides

6 < 8 < 11

, which angle is largest?

Example 15

medium

In triangle

ABC

\angle A = 2\angle B

and

\angle C = \angle B + 20^\circ

. Find each angle.

∠A

Example 16

medium

Classify the triangle with sides

6, 8, 10

by sides and by angles.

Example 17

medium

In an isosceles triangle, one of the equal angles is

25^\circ

less than the third (vertex) angle. Find all three angles.

Example 18

easy

A triangle has sides

5

5

, and

8

. What type is it (by sides)?

Classify by side lengths: two sides equal 5, base equals 8.

Example 19

medium

Classify the triangle with sides

5

cm,

5

cm, and

8

cm by its sides and determine whether it is acute, right, or obtuse.

Example 20

easy

What is the sum of the interior angles of a triangle?

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Related Concepts

Basic Shapes Angles Pythagorean Theorem Triangles Trigonometric Functions