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The Interior Angles of a Triangle

The Interior Angles of a Triangle

A triangle has 3 interior angles.



The interior angles of a triangle determine the type of triangle.

The interior angles of a triangle add up to 180°.

Interior Angles and the Type of Triangles

Triangles are equilateral, isosceles or scalene depending on how many of the interior angles are equal to each other.



Triangles are acute, obtuse or right depending on how whether all angles are less than 90°, 1 angle is more than 90° or 1 angle is equal to 90°.



Read more about the types of triangles

The Interior Angles of a Triangle Add Up to 180°

The interior angles of any triangle add up to 180°.



A Real Example of How the Interior Angles of a Triangle Add Up to 180°

The interior angles of the triangle below add up to 180°.
50° + 60° + 70° = 180°.



How to Find a Missing Interior Angle of a Triangle

Because all the interior angles of a triangle add up to 180°, it is possible to find a missing interior angle when the others are known.

Question: What is the missing angle, x, in the triangle below?



Step 1: Add up the interior angles of the triangle and make this equal to 180°.
75° + 50° + x = 180°.

Step 2: Rearrange the equation to find x.
x = 180° - 75° - 50° = 55°.



Read more about how to find a missing angle in a triangle

More on the Interior Angles of Triangles

The slider below shows more about the interior angles of a triangle:
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Note
WHAT IS A TRIANGLE?

A triangle is a 2-dimensional shape with three sides and three angles.



HOW TO FIND THE MISSING ANGLE OF A TRIANGLE

The interior angles of a triangle always add up to 180°.



where A, B and C are the interior angles of a triangle.

A + B + C = 180°

is an algebraic equation.

When 2 of the 3 angles are known, the 3rd angle can be found by substituting the known values into the equation and then rearranging the equation.

Consider the triangle below:



Find C.

A + B + C = 180°

We know A = 45, B = 55.

45° + 55° + C = 180°

This is an algebraic equation that contains addition.

The 45° and 55° are being added to C.

Subtract them from both sides to make C the subject of the equation.

C = 180° - 45° - 55°

C = 80°