In the given figure, AB//CD. Find the values of x, y and z.
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It is given that AB∥CD and EF is a transversal
from the fiture we know that ∠AEF and∠EFG are alternate angles
so we get
∠AEF=∠EFG=75
o
∠EFG=y=75
o
from the figure we know that ∠EFC and ∠EFG form a linear pair of angles
so we get
∠EFC+∠EFG=180
o
it can also be written as
x+y=180
o
by substituting the value of y we get
x+75
o
=180
o
x=105
o
from the figure based on the exterior angle property it can be written as
∠EGD=∠EFG+∠FEG
by substituting the values in the above equation we get
125
o
=y+z
125
o
=75
o
+z
z=50
o
therefore the values of x,y,z are 105
o
,75
o
,50
o
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