Final answer:
Considering the sum of angles in a triangle is 180º, the value of ∠K would be less than 44º, as it is derived by subtracting ∠J from 180º. None of the provided options are valid since they all exceed 44º.
Step-by-step explanation:
To find the values of ∠K in triangle ΔJKL, we use the fact that the sum of angles in a triangle is always 180°. Given ∠J = 136º and the lengths of the sides j = 49 cm and k = 53 cm, we don't need the side lengths as they do not directly help in finding the angle measures. We can calculate ∠K by subtracting ∠J from 180°.
∠K = 180° - ∠J - ∠L
Since we don't have the measure of ∠L, we can say:
∠K = 180° - 136° - ∠L
It's not possible to solve for ∠K without additional information about ∠L or side l. However, if we assume that the triangle is a non-degenerate triangle, then both ∠K and ∠L must be greater than 0° and less than 180° - ∠J. This means that ∠K must be less than:
∠K < 180° - 136°
∠K < 44°
None of the options provided (72º, 73º, 74º, 75º) are possible because they are all greater than 44°. There seems to be an error in the question or the options given.