Question

Find the value of $x$ and $y$ from the figure.

Answer 1

The given figure is

$\angle ABC+\angle CBD={180}^{\circ }$ (Supplementary angles)

$\Rightarrow {120}^{\circ }+\angle CBD={180}^{\circ }\Rightarrow \angle CBD={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

Since, $\angle EDF=\angle CBD$ (Corresponding angles)

$x={60}^{\circ }$

Also $\angle DGH=\angle EDF$ (Corresponding angles)

$3y+6^{\circ }=x$

$3y+6^{\circ }={60}^{\circ }3y={60}^{\circ }-6^{\circ }={54}^{\circ }y=\frac{{54}^{\circ }}{3}={18}^{\circ }$