see the attached figure to better understand the problem
In the figure
Angle A and Angle B are vertical angles
so
∠A=∠B
Angle C and Angle D are vertical angles
so
∠C=∠D
Angle A and Angle C are supplementary angles
so
∠A+∠C=[tex]180\°[/tex]
Angle D and Angle B are supplementary angles
so
∠D+∠B=[tex]180\°[/tex]
therefore
∠A+∠C+∠D+∠B=[tex]360\°[/tex]
the answer is the option C
[tex]360\°[/tex]
