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)