Answer:
The answer is 76.
Step-by-step explanation:
≅ means to be equal to.
☆Angle DGE ≅ EGF.
Therefore, 3x + 8 = 5x - 12
☆Let's solve that equation.
[tex]3x + 8 = 5x - 12 \\ \frac{ - 5x \: \: \: \: \: \: \: = - 5x \: \: \: \: \: \: \: \: }{ - 2x + 8 = - 12} \\ \frac{ \: \: \: \: \: \: \: \: - 8 = - 8}{ \frac{ - 2x}{ - 2} = \frac{ - 20}{ - 2} } \\ x = 10[/tex]
We found the value of x which is 10.
☆Let's Now plug in.
[tex]DGE \\ 3x + 8 \\ 3(10) + 8 \\ 30 + 8 \\ 38[/tex]
and the other:
[tex]EGF \\ 5x - 12 \\ 5(10) - 12 \\ 50 - 12 \\ 38[/tex]
☆They asked for what the angle of DGF measured. So we would have to add both sides
[tex]38 + 38 = 76[/tex]
☆The answer is 76
