In this post we will first discuss the concept of exterior angles of quadrilateral and then try to find the sum of all the exterior angles.

## Exterior angles of quadrilateral

Exterior angles are formed between one side of quadrilateral and extended side of the other side.

Consider the above quadrilateral ABCD.

Here ∠1 is the exterior angle of quadrilateral formed between side BC and adjacent extended side CE.

In quadrilateral, there are 4 exterior angles.

In the above quadrilateral, ∠1, ∠2, ∠3 and ∠4 are the four exterior angles drawn.

### Interior & Exterior angle of quadrilateral form linear pair

In any quadrilateral, when you see closely you will find that both the adjacent interior & exterior angle form linear pair.

This mean that sum of adjacent interior & exterior angle of quadrilateral measure 180 degree.

Consider the above quadrilateral ABCD.

Here ∠1 is the interior and ∠2 is the exterior angle.

You can see that both the angles are forming linear pair. So we can write;

∠1 + ∠2 = 180 degree

This is very powerful concept and it helps you to solve variety of quadrilateral related questions. So make sure to remember the concept.

### Sum of exterior angle of quadrilaterals

The sum of all four exterior angle of quadrilateral measures 360 degree.

Consider the above quadrilateral with exterior angles.

Here;

∠1 + ∠2 + ∠3 + ∠4 = 360 degree

It’s a very important concept. Please remember it for your examination.

### Questions on angle of quadrilateral

**Question 01**

Find the value of exterior angle of quadrilateral if the adjacent interior angle measure 60 degree.

**Solution**

We know that in quadrilateral, adjacent interior and exterior angle form linear pair.

∠A + ∠x = 180

60 + x = 180

x = 120 degree

Hence, the exterior angle measures 120 degree.

**Question 02**

In the below quadrilateral, find the measure of angle x.

**Solution**

We know that in quadrilateral the sum of exterior angle measures 360 degree.

120 + 40 + 120 + x = 360

280 + x = 360

x = 360 – 280

x = 80 degree

Hence, the exterior angle measures 80 degree.

**Question 03**

Find the measure of angle x in below figure.

**Solution**

We know that sum of interior angle of quadrilateral measure 360 degree.

∠A + ∠B + ∠C + ∠D = 360

80 + 70 + 100 + x = 360

260 + x = 360

x = 360 – 260

x = 100 degree

In quadrilateral, alternate interior & exterior angle form linear pair.

x + y = 180

100 + y = 180

y = 180 – 100

y = 80 degree

Hence, the required exterior angle measures 80 degrees.