Find the value of the unknown exterior angles x in the following diagrams:




(i) It is given in the question that,


1st interior angle = 50o and 2nd interior angle = 70o


Note: According to exterior angle theorem,


The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.


Exterior angle = x


Sum of interior angles = 50o + 70o


Thus, using exterior angle theorem,


x = 50o + 70o


x = 120o


The value of x is 120o


(ii) It is given in the question that,


1st interior angle = 65o and 2nd interior angle = 45o


Note: According to exterior angle theorem,


The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.


Exterior angle = x


Sum of interior angles = 65o + 45o


Using, exterior angle theorem, we have


x = 65o + 45o


x = 110o


Hence, the value of x is 110o


(iii) It is given in the question that,


1st interior angle = 30o and 2nd interior angle = 40o


Note: According to exterior angle theorem,


The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.


Exterior angle = x


Sum of interior angles = 30o + 40o


Using exterior angle theorem, we have


x = 30o + 40o


x = 70o


Hence, the value of x is 70o


(iv) It is given in the question that,


1st interior angle = 60o and 2nd interior angle = 60o


Note: According to exterior angle theorem,


The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.


Exterior angle = x


Sum of interior angles = 60o + 60o


Using exterior angle theorem, we have


x = 60o + 60o


x = 120o


Hence, the value of x is 120o


(v) It is given in the question that,


1st interior angle = 50o and 2nd interior angle = 50o


Note: According to exterior angle theorem:


The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.


Exterior angle = x


Sum of interior angles = 50o + 50o


Using exterior angle theorem, we have


x = 50o + 50o


x = 100o


Hence, the value of x is 100o


(vi) It is given in the question that,


1st interior angle = 30o and 2nd interior angle = 60o


Note: According to exterior angle theorem:


The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.


Exterior angle = x


Sum of interior angles = 30o + 60o


Using, exterior angle theorem, we have


x = 30o + 60o


x = 90o


Hence, the value of x is 120o


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