Mathematics

In the given figure, $$AB\parallel CD$$. Find the values of $$x,y$$ and $$z$$.


SOLUTION
It is given that $$AB\parallel CD$$ and $$EF$$ is a transversal
from the fiture we know that $$\angle AEF$$ and$$\angle EFG$$ are alternate angles

so we get

$$\angle AEF=\angle EFG={ 75 }^{ o }$$

$$\angle EFG=y={75}^{o}$$

from the figure we know that $$\angle EFC$$ and $$\angle EFG$$ form a linear pair of angles

so we get

$$\angle EFC+\angle EFG={ 180 }^{ o }$$

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

$$\angle EGD=\angle EFG+\angle FEG$$

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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