Final answer:
The measurements that could create more than one triangle are given in options A and C.
Step-by-step explanation:
To determine which measurements could create more than one triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Let's analyze each option:
Option A: The sum of the two given sides, 5cm and 10cm, is 15cm which is greater than the third side (40 degrees is irrelevant for this analysis). Therefore, this option can form a triangle.
Option B: The sum of the two smaller sides, 4 inches and 8 inches, is 12 inches which is less than the longest side of 15 inches. Therefore, this option cannot form a triangle.
Option C: The sum of the two smaller sides, 6 inches and 8 inches, is 14 inches which is greater than the longest side of 10 inches. Therefore, this option can form a triangle.
Option D: The sum of the three angles in a triangle is always 180 degrees. However, the given angles in this option add up to 180 degrees, so this option cannot form a triangle.
Based on the analysis, the measurements that could create more than one triangle are Option A (5cm, 10cm, and 40 degrees) and Option C (6 inches, 8 inches, and 10 inches).