##### Find the values of the unknowns x and y in the following diagrams:

(i) From the given figure, we have

y + 120o = 180o (Linear pair)

Therefore,

y = 180o – 120o

y = 60o

x + y + 50o = 180o (angle sum property of triangle)

x + 110o = 180o

x = 180o – 110o

x = 70o

Hence,

The value of x = 70o

And,

Value of y = 60o

(ii) From the given figure, we have

y = 80o (Vertically opposite angle)

y + x + 50o = 180o (angle sum property of triangle)

80o + x + 50o = 180o

130o + x = 180o

x = 180o – 130o

x = 50o

Hence,

The value of x = 50o

And,

The value of y = 80o

(iii) From the given figure,

y + 50o + 60o = 180o (angle sum property of triangle)

y + 110o = 180o

y = 180o – 110o

y = 70o

x and y are on a straight line and forming a linear pair

Therefore,

x + y = 180o

x + 70o = 180o

x = 180o – 70o

x = 110o

Hence,

The value of x = 110o

And,

Value of y = 70o

(iv) From the given figure, we have

x = 60o (Vertically opposite angle)

30o + x + y = 180o (angle sum property of triangle)

30o + 60o + y = 180o

90o + y = 180o

y = 180o – 90o

y = 90o

Hence,

The value of x = 60o

And,

Value of y = 90o

(v) From the given figure, we have

y = 90o (Vertically opposite angle)

x + x + y = 180o (angle sum property of triangle)

2x + y = 180o

2x + 90o = 180o

2x = 180o – 90o

2x = 90o

x =

x = 45o

Hence, The value of x = 45o

And,

The valuue of y = 90o

(vi) From the given figure, we have

y = x (Vertically opposite angles)

a = x (Vertically opposite angles)

b = x (Vertically opposite angles)

a + b + x = 180o (angle sum property of triangle)

x + x + x = 180o

3x = 180o

x =

x = 60o

y = x (Vertically opposite angle)

Hence,

The value of y = x = 60o

8