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

(i) In the above question, we have

1^{st} interior angle = x, 2^{nd} interior angle = 50^{o} and 3^{rd} interior angle = 60^{o}

We have to find out the value of x

Thus,

x + 50^{o} + 60^{o} = 180^{o} (angle sum property of triangle)

x + 110^{o} = 180^{o}

x = 180^{o} – 110^{o}

x = 70^{o}

Hence, the value of x is 70^{o}

(ii) In the above question, we have

1^{st} interior angle = x, 2^{nd} interior angle = 90^{o} and 3^{rd} interior angle = 30^{o}

We have to find out the value of x

Thus,

x + 90^{o} + 30^{o} = 180^{o} (angle sum property of triangle)

x + 120^{o} = 180^{o}

x = 180^{o} – 120^{o}

x = 60^{o}

Hence, the value of x is 60^{o}

(iii) In the above question, we have

1^{st} interior angle = x, 2^{nd} interior angle = 30^{o} and 3^{rd} interior angle = 110^{o}

We have to find out the value of x

Thus,

x + 30^{o} + 110^{o} = 180^{o} (angle sum property of triangle)

x + 140^{o} = 180^{o}

x = 180^{o} – 140^{o}

x = 40^{o}

Hence, the value of x is 40^{o}

(iv) In the above question, we have

1^{st} interior angle = 50^{o,} 2^{nd} interior angle = xand 3^{rd} interior angle = x

We have to find out the value of x

Thus,

50^{o} + x + x = 180^{o} (angle sum property of triangle)

2x + 50^{o} = 180^{o}

2x = 180^{o} – 50^{o}

2x = 130^{o}

x =

x = 65^{o}

Hence, the value of x is 65^{o}

(v) In the above question, we have

1^{st} interior angle = x, 2^{nd} interior angle = x and 3^{rd} interior angle = x

We have to find out the value of x

And,

x + x + x = 180^{o} (angle sum property of triangle)

3x = 180^{o}

x =

x = 60^{o}

Hence, the value of x is 60^{o}

(vi) In the above question, we have

1^{st} interior angle = x, 2^{nd} interior angle = 2x and 3^{rd} interior angle = 90^{o}

We have to find out the value of x

Thus,

x + 2x + 90^{o} = 180^{o} (angle sum property of triangle)

3x + 90^{o} = 180^{o}

3x = 180^{o} – 90^{o}

3x = 90^{o}

x =

x = 30^{o}

Hence, the value of x is 30^{o}

7