Answer:
∠SVT = 17° ∠VUT =143°
Explanation:
system of Eq.
Eq. 1) 20 + 8x-49 +y =180 ( around one triangle)
8x +y = 209 (Eq 1 simplified)
16x +2y =418 (Eq 1 times 2)
Eq. 2) 40 +8x-49 + 5x+23 +2y =360 (around the whole diamond )
13x + 2y = 346 (Eq 2 simplified)
-(16x +2y = 418 ) ( subtract Eq. 1 from Eq. 2 )
-3x = -72
x = 24°
then ∠S = 5x+23 = 5(24) +23 = 143°
then ∠U = 8x -49 = 8(24) - 49 = 143°
20 + 143 +y =180
y = 17°
check it :
40 + 34 + 286 = 360° ( around the whole diamond )
:) looks good