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

(i) It is given in the question that,

1st interior angle = x 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 = 115o

Sum of interior angles = x + 50o

Using exterior angle theorem, we have

115o = x + 50o

x = 115o – 50o

x = 65o

Hence, the value of x is 65o

(ii) It is given in the question that,

1st interior angle = 70o and 2nd 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 = 100o

Sum of interior angles = 70o + x

Using exterior angle theorem, we have

100o = 70o + x

x = 100o – 70o

x = 30o

Hence, the value of x is 30o

(iii) It is given in the question that,

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

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 = 125o

Sum of interior angles = x + 90o

Using exterior angle theorem, we have

125o = x + 90o

x = 125o – 90o

x = 35o

Hence, the value of x is 35o

(iv) It is given in the question that,

1st interior angle = x 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 = 120o

Sum of interior angles = x + 60o

Using exterior angle theorem, we have

120o = x + 60o

x = 120o – 60o

x = 60o

Hence, the value of x is 60o

(v) It is given in the question that,

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

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 = 80o

Sum of interior angles = x + 30o

Using exterior angle theorem, we have

80o = x + 30o

x = 80o – 30o

x = 50o

Hence, the value of x is 50o

(vi) It is given in the question that,

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

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 = 75o

Sum of interior angles = x + 35o

Using exterior angle theorem, we have

75o = x + 35o

x = 75o – 35o

x = 40o

Hence, the value of x is 40o

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