Angles Of A Triangle

The angles of a triangle have the following properties:

Property 1: The sum of the 3 angles in a triangle is always 180˚.

Example :

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

Example :

Property 3 . An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Example :

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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