Is this correct?

[Ciarán]

 

[MarkFL]

I would write:

[MATH]\angle efd+38^{\circ}+65^{\circ}=180^{\circ}[/MATH]
[MATH]\angle efd=(180-103)^{\circ}[/MATH]
[MATH]\angle efd=77^{\circ}\quad\checkmark[/MATH]
[MATH]\frac{\overline{ef}}{\sin(38^{\circ})}=\frac{80}{\sin(77^{\circ})}[/MATH]
[MATH]\overline{ef}=\frac{80\sin(38^{\circ})}{\sin(77^{\circ})}\approx50.548[/MATH]
You didn't use the angle opposing the side of length 80.

 

[Ciarán]

I would write:

[MATH]\angle efd+38^{\circ}+65^{\circ}=180^{\circ}[/MATH]
[MATH]\angle efd=(180-103)^{\circ}[/MATH]
[MATH]\angle efd=77^{\circ}\quad\checkmark[/MATH]
[MATH]\frac{\overline{ef}}{\sin(38^{\circ})}=\frac{80}{\sin(77^{\circ})}[/MATH]
[MATH]\overline{ef}=\frac{80\sin(38^{\circ})}{\sin(77^{\circ})}\approx50.548[/MATH]
You didn't use the angle opposing the side of length 80.

Thank you

 

[Steven G]

You wrote 38+65 =103 + 77 = 180.
Maybe 103 + 77 =180, but 38+65 \(\displaystyle \neq\)103+77 !! Rather 38+65 = 103.

Equal signs must be valid!!

 

[lookagain]

. . .

I would write:

[MATH]m\angle efd+38^{\circ}+65^{\circ}=180^{\circ}[/MATH]
[MATH]m\angle efd=(180-103)^{\circ}[/MATH]
[MATH]m\angle efd=77^{\circ}\quad\checkmark[/MATH]
We are referring to the aspect of the angles involving the number
of their degrees, or the measure of each angle.

 

[MarkFL]

I suppose we could then use, if we so choose:

[MATH]\measuredangle efd[/MATH]