Explanation:
let's use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
so,
5.4/sin(K/2) = 12.3/sin(M1)
8.2/sin(K/2) = x/sin(M2)
M1 + M2 = 180 (as complementary angles or linear pair)
M2 = 180 - M1
sin(K/2) = 5.4×sin(M1)/12.3
sin(K/2) = 8.2×sin(M2)/x
therefore
5.4×sin(M1)/12.3 = 8.2×sin(180 - M1)/x
since sin(a) = sin(180 - a)
5.4×sin(M1)/12.3 = 8.2×sin(M1)/x
and then
5.4/12.3 = 8.2/x
x×5.4 = 8.2×12.3
x = 8.2×12.3/5.4 = 18.67777777... ≈ 18.7