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

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)

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 :

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

The above angle properties would enable us to find unknown angles.

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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