Respuesta :
Answer:
37°
Step-by-step explanation:
We know that [tex]\angle VST[/tex] and [tex]\angle VUT[/tex] are opposite angles in a quadrilateral.
If we assume that the quadrilateral is a parallelogram, then those angles are equal, so
[tex]\angle VST = \angle VUT\\5x+23=8x-49[/tex]
Then, we solve for [tex]x[/tex]
[tex]23+49=8x-5x\\3x=72\\x=\frac{72}{3}\\ x=24[/tex]
Now, we use this value to find VST angle
[tex]\angle VST=5x+23=5(24)+23=143\°[/tex]
On the other hand, the sum of all four internal angles can be expressed as
[tex]2(\angle VST)+2(\angle SVT)=360\°[/tex]
Solving for SVT
[tex]2(143)+2(\angle SVT)=360\°\\\angle SVT = \frac{360\° - 286\°}{2}=37\°[/tex]
Therefore, the answer is 37°.
