Triangles Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Triangles.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept 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.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Triangles are rigid and stable—the basis of structural engineering.

Common stuck point: Angle sum is always exactly 180° regardless of triangle shape—scalene, isosceles, or equilateral.

Sense of Study hint: Draw a triangle, tear off all three corners, and arrange them in a row to see they form a straight line (180 degrees).

Worked Examples

Example 1

easy
Two angles of a triangle measure 50° and 65°. Find the third angle.

Solution

  1. 1
    The angle sum property states that all angles in a triangle add up to 180°.
  2. 2
    Let the third angle be x: 50 + 65 + x = 180.
  3. 3
    Solve: x = 180 - 115 = 65°.

Answer

x = 65°
The triangle angle sum property (180°) is one of the foundational facts in geometry. Since two angles are 50° and 65°, and the third is also 65°, this is an isosceles triangle.

Example 2

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.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
An equilateral triangle has a perimeter of 36 cm. Find the length of each side.

Example 2

medium
The three angles of a triangle are in the ratio 2:3:4. Find the measure of each angle.
← Back to Triangles Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

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