since two of the triangles are similar that means they are the same thing :
<A = <L
108 = 108
<C is twice from <M so :
<C is 2x < M is x
as you note down the answer you can draw two triangles and label them according to thier values, you will see that triangle ABC has two things now ;
a = 108 and c = 2x
when you have two measures in a triangle you can find the 3rd one :
suppose that third < of triangle ABC is x ;
108 + 2x + x = 180
108 + 3x = 180
3x = 180 - 108
3x = 72
x = 24 <m = 24
further if you want to find C : < c = 2x
< c = 2 ( 24 )
< c = 48
