Final answer:
Option B) with three sides measuring 14 m, 11 m, and 18 m can create only one unique triangle.
Step-by-step explanation:
To create a unique triangle, you need to consider the measure of angles or the lengths of sides. So, let's analyze each option:
A) Three angles measuring 75°, 45°, and 50°: These angles do not add up to 180°, so they cannot create a triangle.
B) Three sides measuring 14 m, 11 m, and 18 m: The sum of any two sides of a triangle must be greater than the third side according to the Triangle Inequality Theorem. In this case, 14 + 11 = 25, which is greater than 18. Therefore, a triangle can be formed.
C) Three angles measuring 400°, 509°, and 60°: These angles sum up to 969°, which is greater than 180°. Thus, they cannot create a triangle.
D) Three sides measuring 3 cm, 4 cm, and 8 cm: The sum of any two sides of a triangle must be greater than the third side. In this case, 3 + 4 = 7, which is less than 8. Therefore, a triangle cannot be formed.
Based on this analysis, only option B) can create a unique triangle.