Question

In the figure, if $AB\left|\right|DEandBD\left|\right|FG$ such that $\angle FGH={125}^{\circ }$ and $\angle B={55}^{\circ },$ find x and y.

Answer 1

In the figure, $AB\left|\right|DEandBD\left|\right|FG$

$\angle FGH={125}^{\circ }$ and $\angle B={55}^{\circ }$

$\angle FGH+FGE={180}^{\circ }$ (Linear pair)

$\Rightarrow {125}^{\circ }+y={180}^{\circ }$

$\Rightarrow y={180}^{\circ }-{125}^{\circ }={55}^{\circ }$

$\because BA\left|\right|FDandBD\left|\right|FG$

$\therefore \angle B=\angle F={55}^{\circ }$

Now in $\Delta EFG,$

$\angle F+\angle FEG+\angle FGE={180}^{\circ }$

(Angles of a triangle)

$\Rightarrow {55}^{\circ }+x+{55}^{\circ }={180}^{\circ }$

$\Rightarrow x+{110}^{\circ }={180}^{\circ }$

$\therefore x={180}^{\circ }-{110}^{\circ }={70}^{\circ }$

Hence x=70,y=${55}^{\circ }$