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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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87

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