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Properties of the Angles Of A Triangle





In these lessons, we will give a summary of the properties of the angles of a triangle.
  • Triangle Sum Theorem - The sum of the 3 angles in a triangle is always 180°
  • The sum of an interior angle and its adjacent exterior angle is 180°
  • Exterior Angle Theorem - An exterior angle of a triangle is equal to the sum of the two opposite interior angles
  • An equilateral triangle has 3 equal angles that are 60° each. An isosceles triangle has 2 equal angles, which are the angles opposite the 2 equal sides

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The angles of a triangle have the following properties:

Property 1: Triangle Sum Theorem - The sum of the 3 angles in a triangle is always 180°.

Example :


The follwing video shows how to prove that the sum of the angles of a triangle is 180 degrees. (Triangle Sum Theorem)



How to Find the Missing Angle in a Triangle Using the Triangle Sum Theorem.





Property 2: The sum of an interior angle and its adjacent exterior angle is 180°.

Example :



Property 3: Exterior Angle Theorem - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Example :


Exterior Angles of a Triangle: Finding the Unknown Angle of a Triangle



The follwing video shows how to use the Exterior Angle Theorem to solve problems involving angles in a triangle.




 

Property 4: Also, recall that an equilateral triangle has 3 equal angles that are 60° each. An isosceles triangle has 2 equal angles, which are the angles opposite the 2 equal sides

How to Find the Missing Angle in an Isosceles Triangle.


Parallel Lines and the Triangle Angle-Sum Theorem.




The above angle properties can help us to find unknown angles in a triangle.

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°


Example :

Find the values of x and y in the following triangle.

Solution:

x + 50° = 92° (sum of opposite interior angles = exterior angle)
x = 92° – 50° = 42°

y + 92° = 180° (interior angle + adjacent exterior angle = 180°.)
y = 180° – 92° = 88°




 


You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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