Final answer:
Option B (a triangle with two given sides and an included angle) can create more than one triangle by varying the length of the third side, while options A, C, and D do not offer this possibility.
Step-by-step explanation:
The question at hand involves the principle that the sum of the angles in any triangle must equal 180 degrees, and the side lengths must adhere to the triangle inequality theorem (the sum of the lengths of any two sides of a triangle must be greater than the length of the third side).
- Option A: A triangle with sides measuring 3 cm, 8 cm, and 15 cm cannot form a triangle because 3 + 8 < 15, violating the triangle inequality theorem.
- Option B: A triangle with sides 10 cm and 20 cm and an included angle of 50° can create more than one triangle because varying the length of the third side can produce different triangle shapes while maintaining the same included angle.
- Option C: A triangle with angles measuring 110°, 40°, and 30° cannot be altered. Adding these angles will always total 180 degrees, creating only one unique triangle.
- Option D: A triangle with angles measuring 100°, 10°, and 70° will also total 180 degrees and produce only one unique triangle.
Therefore, among the options provided, Option B can create more than one triangle through adjustments of the third side, while the other options cannot.