Final answer:
In triangle TUV, the angles are given by (2x + 20)°, (8x + 12)°, and (3x + 19)°. By solving for x and substituting it back into the angle measures, we find that angle TUV measures 34°, angle UVW measures 68°, and angle VTU measures 40°. Therefore, we can label the triangle correctly as TUVW.
Step-by-step explanation:
In triangle TUV, TV is extended through point V to point W. To label the triangle correctly according to the description, we need to determine which angles belong to which vertices. Given that m∠TUV = (2x + 20)°, m∠UVW = (8x + 12)°, and m∠VTU = (3x + 19)°, we can set up the following equations:
2x + 20 + 8x + 12 + 3x + 19 = 180
Solving the equation gives x = 7. Substituting x back into the given angle measures:
m∠TUV = (2(7) + 20)° = 34°
m∠UVW = (8(7) + 12)° = 68°
m∠VTU = (3(7) + 19)° = 40°
Therefore, in triangle TUV, angle TUV measures 34°, angle UVW measures 68°, and angle VTU measures 40°. We can now label the triangle correctly as shown:
T (34°)
U (40°)
V (68°)
W