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 1212?

Example 2

hard
Triangle ABCABC has ∠A=40∘\angle A = 40^\circ and the bisector of ∠B\angle B meets ACAC at DD so that ∠BDA=100∘\angle BDA = 100^\circ. Find ∠C\angle C.

Example 3

easy
Two angles of a triangle are 50∘50^\circ and 60∘60^\circ. Find the third angle.

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 xx, x+10∘x + 10^\circ, and x+20∘x + 20^\circ. Is the triangle acute, right, or obtuse?

Example 7

easy
Can a triangle have two right angles?

Example 8

easy
An isosceles triangle has a vertex angle of 40∘40^\circ. Find each base angle.

Example 9

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

Example 10

easy
One angle of a triangle is 90∘90^\circ. What type is it (by angles)?

Example 11

medium
An exterior angle of a triangle is 130∘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 2:3:42:3:4. Find the measure of each angle.

Example 13

challenge
In triangle ABCABC, ∠B=50∘\angle B = 50^\circ and ∠C=30∘\angle C = 30^\circ. Point DD lies on side BCBC such that AD=BDAD = BD. Find ∠DAC\angle DAC.

Example 14

medium
In a triangle, the largest angle is opposite the longest side. If a triangle has sides 6<8<116 < 8 < 11, which angle is largest?

Example 15

medium
In triangle ABCABC, ∠A=2∠B\angle A = 2\angle B and ∠C=∠B+20∘\angle C = \angle B + 20^\circ. Find each angle.

Example 16

medium
Classify the triangle with sides 6,8,106, 8, 10 by sides and by angles.

Example 17

medium
In an isosceles triangle, one of the equal angles is 25∘25^\circ less than the third (vertex) angle. Find all three angles.

Example 18

easy
A triangle has sides 55, 55, and 88. What type is it (by sides)?

Example 19

medium
Classify the triangle with sides 55 cm, 55 cm, and 88 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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