Question

In the adjacent figure $AB||CD$. Find the values of $x,y$ and $z$.

Answer 1

Given $\angle AEP+\angle PEC+\angle BEC={180}^{\circ }$ (Supplementary angles or angle of a straight line )
$x^{\circ }+{70}^{\circ }+x^{\circ }={180}^{\circ }{2x}^{\circ }={180}^{\circ }-{70}^{\circ }={110}^{\circ }x=\frac{{110}^{\circ }}{2}={55}^{\circ }$

$\angle CEB+\angle ECD={180}^{\circ }$ (Angles made on same side of parallel lines or consecutive interior angles )

$x+z={180}^{\circ }{55}^{\circ }+z={180}^{\circ }z={180}^{\circ }-{55}^{\circ }={125}^{\circ }$

In $\Delta APE$, the sum of interior angles is equals to $={180}^{\circ }$
$\angle APE+\angle PEA+\angle PAE={180}^{\circ }$

$y+x+{90}^{\circ }={180}^{\circ }y+{55}^{\circ }+{90}^{\circ }={180}^{\circ }y+{145}^{\circ }={180}^{\circ }y={180}^{\circ }-{145}^{\circ }={35}^{\circ }$