Q. 24.6( 149 Votes )

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






Answer :

(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 + 60+ 50o = 180o

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

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