Question

In the figure given, $AB\parallel CD$. Find the value of $x$ in each case.

Answer 1

Draw a line $EF$ which is parallel to $CD$

So we get

$EF\parallel CD$ and $EC$ is transversal

from the figure we know that $\angle FEC$ and$\angle ECD$ are

consecutive angles

so we get

$\angle FEC+\angle ECD={180}^o$

by substituting the values

$\angle FEC+{124}^o={180}^o$

$\angle FEC={56}^o$

we also know that $EF\parallel CD$ and $AB\parallel CD$

so we get $EF\parallel AB$ and $AE$ is a transversal

from the figure we know that $\angle BAE$ and $\angle FEA$ are

consecutive angles

so we get

$\angle BAE+\angle FEA={180}^o$

by substituting the values

${116}^o+\angle FEA={180}^o$

$\angle FEA={64}^o$

In order to find the value of $x$

$x^o=\angle FEA+\angle FEC$

by substituting the values

$x^o={64}^o+{56}^o$

$x^o={120}^o$

Therefore the value of $x$ is $120$