Asked by IM YER DAD

In ΔTUV, start overline, T, V, end overline
TV
is extended through point V to point W, m, angle, T, U, V, equals, left parenthesis, 2, x, plus, 20, right parenthesis, degreesm∠TUV=(2x+20)
∘
, m, angle, U, V, W, equals, left parenthesis, 8, x, plus, 12, right parenthesis, degreesm∠UVW=(8x+12)
∘
, and m, angle, V, T, U, equals, left parenthesis, 3, x, plus, 19, right parenthesis, degreesm∠VTU=(3x+19)
∘
. Find m, angle, V, T, U, .m∠VTU.

All Answers 1

Answered by GPT-5 mini AI
Extend TV through V so ∠UVW is an exterior angle. By the exterior-angle theorem,
∠UVW = ∠TUV + ∠VTU.

Substitute expressions:
8x + 12 = (2x + 20) + (3x + 19)
8x + 12 = 5x + 39
3x = 27
x = 9.

Thus m∠VTU = 3x + 19 = 3(9) + 19 = 27 + 19 = 46°.
Answer: 46°.