Question

what is the value of t?
work it out
not feeling ready yet? these can help:
triangle angle - sum theorem
classify triangles

Explanation:

Step1: Find the measure of $\angle DEG$

In $\triangle DEG$, use the triangle angle - sum theorem ($\angle D+\angle DEG+\angle DGE = 180^{\circ}$).
Let $\angle DEG=\angle DGE = x$ (since $EG = ED$).
So, $96^{\circ}+x + x=180^{\circ}$.
$96^{\circ}+2x = 180^{\circ}$.
$2x=180^{\circ}-96^{\circ}=84^{\circ}$.
$x = 42^{\circ}$.

Step2: Prove $\triangle FEG\cong\triangle DEG$

Since $FE = DE$, $FG = DG$, $EG = EG$ (SSS congruence criterion), $\triangle FEG\cong\triangle DEG$.

Step3: Find the value of $t$

$\angle FEG=\angle DEG = 42^{\circ}$, $\angle FGE=\angle DGE = 42^{\circ}$.
In $\triangle FEG$, using the triangle angle - sum theorem ($\angle F+\angle FEG+\angle FGE = 180^{\circ}$).
$t + 42^{\circ}+57^{\circ}=180^{\circ}$.
$t=180^{\circ}-(42^{\circ}+57^{\circ})$.
$t = 42^{\circ}$.

Answer:

$42$