Question

In the adjacent figure AB || CD, EF $\perp$ CD and $\angle GED={126}^o$, find $\angle AGE,\angle GEF$ and $\angle FGE$.

Answer 1

$\angle AGE=\angle GED={126}^{\circ }$ (Alternate angles)

$\angle GED=\angle GEF+\angle FED$

${126}^{\circ }=\angle GEF+{90}^{\circ }$

$\angle GEF={126}^{\circ }-{90}^{\circ }={36}^{\circ }$

$\angle CEG+\angle GED={180}^{\circ }$ (Supplementary angles)

$\angle CEG+{126}^{\circ }={180}^{\circ }$

$\angle CEG={180}^{\circ }-{126}^{\circ }={54}^{\circ }$

$\angle FGE=\angle CEG={54}^{\circ }$ (Alternate angles )