Question

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

Answer 1

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 ${105}^o,{75}^o,{50}^o$