Properties of the Angles Of A Triangle



In this lesson, 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°





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