Verified answer

Well,

Apply the formula :

sin(90° - x) = cos(x)

so here :

90 - (2x + 14) = x + 16

90 - 2x - 14 = x + 16

90 - 14 - 16 = x + 2x

3x = 60

x = 60/3

x = 20°

qed

hope it' ll help !!

sin(x+16)=cos(2x+14)

sin(x+16/1)

sin(x+16)=sin(90-(2x+14))

x+16=90-(2x+14)

x+16+(2x+14)=90

3x+30=90

3x=60

X=20

sin(t) = cos(90-t). Put t = x+16 and 90-t = 2x+14, ie., t = 90 - 2x -14 = x+16, ie., 60 = 3x, ie., x = 20 deg.

Well, assuming that the two angles are acute angles, then they are complementary (add to 90°):

x + 16 + 2x + 14 = 90

3x + 30 = 90

3x = 60

x = 60/3

x = 20

Answer:

x = 20

(The two angles are 36° and 54°)