Question

In the figure below, ZABC = ZDEC and ZGFE = ZDCE. Point Cis the point of intersectionbetween AG and BD, while point E is the point of intersection between AG and DF

Answer 1

From the information provided, we can deduce the following;

Note that

`\begin{gathered} \angle ABC=\angle DEC \\ \text{Both angles are marked in red as shown in the attachment} \end{gathered}`

Also, note that

`\begin{gathered} \angle GFE=\angle DCE \\ \text{Both angles are marked in blue} \end{gathered}`
`\angle ACB=\angle DCE\text{ (vertically opposite angles are equal)}`

If angle ACB equals angle DCE, and DCE equals GFE, then it means;

`\angle ACB=\angle GFE`

Similarly;

`\angle GEF=\angle DEC\text{ (Vertically opposite angles are equal)}`

In the same manner as the other angle as explained above,

`\angle GEF=\angle ABC`