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

(i) It is given in the question that,

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

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 = 50^o + 70^o

Thus, using exterior angle theorem,

x = 50^o + 70^o

x = 120^o

∴ The value of x is 120^o

(ii) It is given in the question that,

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

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 = 65^o + 45^o

Using, exterior angle theorem, we have

x = 65^o + 45^o

x = 110^o

Hence, the value of x is 110^o

(iii) It is given in the question that,

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

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 = 30^o + 40^o

Using exterior angle theorem, we have

x = 30^o + 40^o

x = 70^o

Hence, the value of x is 70^o

(iv) It is given in the question that,

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

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 = 60^o + 60^o

Using exterior angle theorem, we have

x = 60^o + 60^o

x = 120^o

Hence, the value of x is 120^o

(v) It is given in the question that,

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

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 = 50^o + 50^o

Using exterior angle theorem, we have

x = 50^o + 50^o

x = 100^o

Hence, the value of x is 100^o

(vi) It is given in the question that,

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

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 = 30^o + 60^o

Using, exterior angle theorem, we have

x = 30^o + 60^o

x = 90^o

Hence, the value of x is 120^o