Angle Sum in a Triangle

House Frame with Triangles
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Building Frames are “triangulated” to give them strength. Without a triangle structure the wood frame will not be rigid or strong.

In Australia, the Sydney Harbor Bridge is made of an interwoven triangle structure.

Sydney Harbour Bridge Triangles
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Every part of the bridge is extensively triangulated to create rigidity and strength.

Sydney Harbor Bridge triangles Detail
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Builders of Structural Frames and Steel Bridges need to have an intimate knowledge of angles and triangles.

In this lesson we look at how the three angles in any triangle always create a total of 180 degrees.


Sum of the Angles in a Triangle

The three angles in any triangle always create a total of 180 degrees.

Two mathematical proofs for angles adding up to 180 degrees in any triangle are shown in the following video.

The first proof involves hands on cutting up a paper triangle, and the second one is a far more technical geometric proof.


The following shows the 180 degrees total rule for several different triangles.

Angle Sum of Triangle
Image Copyright 2012 by Passy’s World


Videos About Triangle Angles

This first video shows several different examples of how to find missing Angles in Triangles.


This next video shows a more complex problem involving Ratios, and how to use an Algebra Equation to solve for the unknown angles.


Here is another video that involves using Algebra to find unknown angles.


Finding an Unknown Angle in a Triangle

Because we know that the three angles add up to 180 degrees, we can easily work out the value for a missing angle.

When a question gives us the values for two interior angles of a triangle, the third missing angle is always 180 minus the two angles that we know.

Missing Angle = 180 minus the other two given angles

The following examples show how to calculate the missing angle for several different triangles, using Algebara equations.

Triangle Sum Examples
Image Copyright 2012 by Passy’s World


Math Warehouse Triangle Interactive

Math Warehouse Triangle Interactive

The middle of the following web page has a drag around interactive which shows the angles always adding to 180, no matter waht shape we make the triangle.

(Much quicker than cutting out lots of random triangles from paper and measuring them).

Note that it is best to set the units button to “Integer” whole numbers when using this demonstration tool.

Click the following link to use this interactive


Finding Angles Worksheet

Click the following link to get a PDF worksheet on finding Triangle Angles.


Finding Angles Game

Tank Attack Angles in Triangles Game

“Tank Attack” has some quite challenging questions on Supplementary Angles, as well as Triangles.

Click the following link to play this game.


Solving Angles Game

Itzi Spider Angles Game

This game about “Itzi” spider involves solving several levels of Angles questions, where later levels include triangles.

Click the following link to play this challenging game.


Related Items

Classifying Triangles
Interactives at Mathwarehouse
Jobs that use Geometry


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