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:*

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:*

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:*

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}

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