Question

In the figure, $AB\parallel CD\parallel EF$ and $AE\perp AB$. Also, $\angle BAE={90}^o$ and $\angle FED={45}^o$. Find the angles x, y and z.

• A. $x={45}^o,y={45}^o,z={135}^o$
• B. $x={135}^o,y={45}^o,z={35}^o$
• C. $x={135}^o,y={135}^o,z={45}^o$
• D. $x={45}^o,y={135}^o,z={45}^o$

Answer 1

The correct option is C $x={135}^o,y={135}^o,z={45}^o$

$\because CD\parallel FE$
$\therefore \angle y+{45}^o={180}^o$ (co-interior angles are supplementary)
$\angle y={135}^o$
$\because CD\parallel AB$
$\angle x=\angle y$ (corresponding angles)
$\therefore \angle x={135}^o$
$\because AB\parallel FE$
$\therefore \angle BAC+\angle AEF={180}^o$ (co-interior angles are supplementary)
$\angle BAC+\angle z+{45}^o={180}^o$
${90}^o+{45}^o+\angle z={180}^o$
$z={180}^o-{135}^o$
$={45}^o$