The correct order of the angles of triangle ABC from largest measure to smallest measure is ∠B, ∠A, and ∠C.
In Mathematics, the length of the opposite side of a triangle would be largest when the interior angle facing it is the largest because the larger an angle, the more vertical the opposite side would become.
Conversely, the length of the opposite side of a triangle would be smallest when the interior angle facing it is the smallest because the smaller an angle, the less vertical the opposite side would become.
By applying the law of cosines, the measure of angle B is given by;

B = 73.6°.
For angle C, we have:

C = 50.9°
By the triangle sum property, we have:
∠A + ∠B + ∠C = 180°
∠A = 180° - (50.9° + 73.6°)
∠A = 55.5°.
By critically observing the triangle shown below, we can logically deduce the following information:
The angle opposite a length of 17 is 50.9° ⇒ ∠C.
The angle opposite a length of 18 is 55.5° ⇒ ∠A.
The angle opposite a length of 21 is 73.6° ⇒ ∠B.
In this context, the correct order of the angles from largest measure to smallest measure is ∠B, ∠A, and ∠C.