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.