The full exercise is attached.
Since JKLM is the result of the rigid motion of ABCD, the two quadrilaterals are congruent, especially their angles.
Therefore:
∡A = ∡J = 82°
∡B = ∡K = 104°
∡C = ∡L = 121°
∡D = ∡M = ?
Recall that the sum of the measure of the angles of a quadrilateral is 360°, and you will find:
∡M = 360 - (∡J + ∡K + ∡L)
= 360 - (82 + 104 + 121)
= 53
Hence, ∠M is 53°.