Question

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

Answer 1

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

So we get

$OF\parallel CD$ and $OD$ is transversal

From the figure we know that $\angle CDO$ and$\angle FOD$ are consecutive angles

So we get

$\angle COD+\angle FOD={180}^o$

By substituting the values

${25}^o+\angle FOD={180}^o$

$\angle FOD={155}^o$

We also know that $OF\parallel CD$ and $AB\parallel CD$

So we get $OF\parallel AB$ and $OB$ is a transversal

From the figure we know that $\angle ABO$ and $\angle FOB$ are consecutive angles

So we get

$\angle ABO+\angle FOB={180}^o$

By substituting the values

${55}^o+\angle FOB={180}^o$

$\angle FOB={125}^o$

In order to find the value of $x$

$x^o=\angle FOB+\angle FOD$

By substituting the values

$x^o={125}^o+{155}^o$

$x^o={280}^o$

Therefore the value of $x$ is ${280}^o$