Interior and Exterior Angles of a Triangle

In this article, we are going to explain interior and exterior angles of a triangle and how to find interior and exterior angles of a triangle with worked examples.

Interior angle:

1) Interior angle of a triangle is an angle formed inside a triangle by two adjacent sides or an angle located within a triangle.
2) A triangle has three interior angles.

Exterior angle:

In a triangle the Exterior angle is an angle formed of linear pair with any one of the angle of the triangle.

triangle

In this diagram, a,b,c and d are interior and exterior angles of a triangle respectively.

Interior angles of a triangle:

In a triangle, the Sum of the three angles inside the triangle always adds up to 180 degrees. The following example will show how to find the interior angles of a triangle.

The total interior angles of triangle = a+b+c = 180°.

Given:

From above figure, find the missing interior angle of a triangle, if the two interior angles of a triangle angle a is 32° and angle b is 34°.

Solution:

So the missing interior angle of a triangle be c.

c + a + b     = 180°  (sum of interior angles of a triangle is equal to 180°)

c + 32° + 34° = 180°

c + 66° = 180°   (subtract 66 both on sides)

c = 180° – 66°

= 114°

Hence the missing interior angle of the triangle c is 114°.

To check:

The total interior angles of a triangle = 114° + 32° + 34°

= 180°.

Exterior angles of a triangle:

In general, the exterior angle of a triangle is always equal to the sum of the two non- adjacent interior angles.

The following example gives a clear view for finding the exterior angle of a triangle.

Given:  From above figure, the two interior angles of a triangle as a is 80° and c is 52°.

To find: The missing interior and exterior angles of a triangle d.

Solution:

Step 1: To find the missing angle of a triangle (Interior angle)

Sum of interior angles of a triangle is equal to 180° or a + b + c = 180°

So the missing Interior angle of triangle be b,

b + 80° + 52° = 180°

b + 132° = 180°     (subtract 132 both on sides)

b = 180° – 132°

= 48°

Interior angle of a triangle b = 48°

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Step 2: To find the Exterior angle of a triangle d.

Exterior angle = 180° - interior angle

d = 180° - b

d = 180° – 48°

d = 132°

Hence the exterior angle of the triangle d = 132°.

Therefore, the interior and exterior angles of a triangle are 80, 48, 52 degrees and 132 degrees.