Find the value of the unknown interior angle x in the following figures:

(i) It is given in the question that,

1^st interior angle = x 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 = 115^o

Sum of interior angles = x + 50^o

Using exterior angle theorem, we have

115^o = x + 50^o

x = 115^o – 50^o

x = 65^o

Hence, the value of x is 65^o

(ii) It is given in the question that,

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

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 = 100^o

Sum of interior angles = 70^o + x

Using exterior angle theorem, we have

100^o = 70^o + x

x = 100^o – 70^o

x = 30^o

Hence, the value of x is 30^o

(iii) It is given in the question that,

1^st interior angle = x and 2^nd interior angle = 90^o

Now, 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 = 125^o

Sum of interior angles = x + 90^o

Using exterior angle theorem, we have

125^o = x + 90^o

x = 125^o – 90^o

x = 35^o

Hence, the value of x is 35^o

(iv) It is given in the question that,

1^st interior angle = x 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 = 120^o

Sum of interior angles = x + 60^o

Using exterior angle theorem, we have

120^o = x + 60^o

x = 120^o – 60^o

x = 60^o

Hence, the value of x is 60^o

(v) It is given in the question that,

1^st interior angle = x and 2^nd interior angle = 30^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 = 80^o

Sum of interior angles = x + 30^o

Using exterior angle theorem, we have

80^o = x + 30^o

x = 80^o – 30^o

x = 50^o

Hence, the value of x is 50^o

(vi) It is given in the question that,

1^st interior angle = x and 2^nd interior angle = 35^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 = 75^o

Sum of interior angles = x + 35^o

Using exterior angle theorem, we have

75^o = x + 35^o

x = 75^o – 35^o

x = 40^o

Hence, the value of x is 40^o