Question

In the given figure, $AB||CD$. Find in degree the value of $x-y+z$. (Input the value without degree)

Answer 1

Given, $AB||CD$, $\angle AEF={75}^{\circ }$

$\angle AEF=\angle EFG={75}^{\circ }$ ....... (Alternate angles)

$y={75}^{\circ }$

$x+y={180}^{\circ }$ ......... (Sum of angles on a straight line is equal to ${180}^{\circ }$)

$x+{75}^{\circ }={180}^{\circ }$

$x={180}^{\circ }-{75}^{\circ }={105}^{\circ }$

From fig, $y+z={125}^{\circ }$

$z={125}^{\circ }-y={125}^{\circ }-{75}^{\circ }={50}^{\circ }$

$\therefore x={105}^{\circ },y={75}^{\circ },$ and $z={50}^{\circ }$

Hence, $x-y+z={80}^{\circ }$