Question

In figure, find $\angle x,\angle y$ and $\angle ACD$ where line $BA\parallel FE.$

Answer 1

$BA\parallel FE$
$\angle x={42}^{\circ }$ (alternate angle)
$\angle ACD=\angle x+{66}^{\circ }$ (ext. angle is equal to sum of opposite interior angles)
$\angle ACD={42}^{\circ }+{66}^{\circ }={108}^{\circ }$
But $\angle y+\angle ACD={180}^{\circ }$
$\angle y={180}^{\circ }-{108}^{\circ }$ (linear pair axiom)
$\angle y={72}^{\circ }$
$\angle x={42}^{\circ }$ and $\angle y={72}^{\circ }$