Interior Angles Of A Triangle
Related Pages
Exterior Angles Of A Triangle
Types Of Triangles
Angles In A Triangle
In these lesson, we will learn
- about interior angles of triangles
- the properties of the interior angles of a triangle
- how the properties can be used to find the missing angles inside a triangle
- how the sum of interior angles of a triangle can be used to set up equations.
Interior Angles
The interior angles of a triangle are the three angles located inside the triangle, at each of its vertices (corners).
The Angle Sum Property
The most fundamental property of the interior angles of any triangle in Euclidean geometry is:
The sum of the measures of the three interior angles of any triangle always equals 180°.
This is also known as the Triangle Angle-Sum Theorem.
The following diagram shows that the sum of angles in a triangle is 180°. Scroll down the page for more examples and solutions on how to find missing angles in a triangle.
Properties of Interior Angles
- The sum of the three interior angles in a triangle is always 180°.
- Since the interior angles add up to 180°, every angle must be less than 180°.
Find missing angles inside a triangle
Why is the Triangle Angle-Sum Theorem important?
Finding Missing Angles: If you know the measure of two angles in a triangle, you can always find the measure of the third angle by subtracting the sum of the known angles from 180°.
Example:
Find the value of x in the following triangle.
Solution:
x + 24° + 32° = 180° (sum of angles is 180°)
x + 56° = 180°
x = 180° – 56° = 124°
Videos
How to find the missing angle inside a triangle.
Example:
Find the missing angle in a triangle.
A = 15°, B = ?, C = 92°
Using Interior Angles Of Triangle To Set Up Equations
How to use the sum of the interior angles of a triangle to solve problems?
Example:
- Write an equation and solve for the unknown.
- Substitute your answer into each expression to determine the measure of the angles.
- Give reasons for your answers.
Using the sum of the interior angles of a triangle, write an equation and solve for the unknown.
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