Final answer:
The correct order of the sides of triangle IKL from smallest to largest is IL (opposite to m∠K=48 degrees), LK (opposite to m∠L=53 degrees), and KL (opposite to m∠I=84 degrees). There's a possible typo in the answer choices, but the solution is deduced from the principles relating angles to their opposite sides in a triangle.
Step-by-step explanation:
The question asks us to list the sides of triangle IKL in order from smallest to largest based on the given angles at each vertex. To solve this, we recall the principle that in any triangle, the side opposite the smallest angle is the shortest side and the side opposite the largest angle is the longest side. Since m∠I=84 degrees is the largest angle, side KL opposite to it would be the longest side. Similarly, the smallest angle is m∠K=48 degrees, meaning side IL opposite to it would be the shortest side. Finally, the remaining side LK opposite to angle L would be of medium length. The correct order from smallest to largest is: IL, LK, KL.
It appears there might be a typo in the answer choices provided, as they mention options such as 'TO' and 'LR' which are not mentioned in the question. Based on the angles provided, we can disregard the typo and provide the correct order of the sides as mentioned above.