Question

If m<VST = (5x + 23) and m<VUT =(8x - 49), find m<SVT​

Answer 1

Answer:17

Step-by-step explanation:

Answer 2

Answer:

37°

Step-by-step explanation:

We know that $\angle VST$ and $\angle VUT$ are opposite angles in a quadrilateral.

If we assume that the quadrilateral is a parallelogram, then those angles are equal, so

$\angle VST = \angle VUT\\5x+23=8x-49$

Then, we solve for $x$

$23+49=8x-5x\\3x=72\\x=\frac{72}{3}\\ x=24$

Now, we use this value to find VST angle

$\angle VST=5x+23=5(24)+23=143\°$

On the other hand, the sum of all four internal angles can be expressed as

$2(\angle VST)+2(\angle SVT)=360\°$

Solving for SVT

$2(143)+2(\angle SVT)=360\°\\\angle SVT = \frac{360\° - 286\°}{2}=37\°$

Therefore, the answer is 37°.