Question

In the given figure, $AB||CD$, then which of the following is always true?

• A. $x=y+z$
• B. $x-y+z=180$
• C. $x+y+z=180$
• D. $z+x=y$

Answer 1

The correct option is B $x-y+z=180$

Draw $EF$ parallel to $AB\text{and}CD$

$x^{\circ }=\angle PRE+\angle QRE$

$=y^{\circ }+{180}^{\circ }-z^{\circ }$

$\Rightarrow x^{\circ }-y^{\circ }+z^{\circ }={180}^{\circ }$