Question

In ΔSTU, start overline, S, U, end overline
SU
is extended through point U to point V, m, angle, U, S, T, equals, left parenthesis, x, plus, 5, right parenthesis, degreesm∠UST=(x+5)
∘
, m, angle, S, T, U, equals, left parenthesis, 2, x, plus, 16, right parenthesis, degreesm∠STU=(2x+16)
∘
, and m, angle, T, U, V, equals, left parenthesis, 6, x, minus, 9, right parenthesis, degreesm∠TUV=(6x−9)
∘
. Find m, angle, S, T, U, .m∠STU.

Answer 1

Since SU is extended through U to V, ∠TUV is an exterior angle of triangle STU. By the exterior-angle theorem,

m∠TUV = m∠UST + m∠STU.

So (6x − 9) = (x + 5) + (2x + 16) = 3x + 21.
Solve: 6x − 9 = 3x + 21 → 3x = 30 → x = 10.

Thus m∠STU = 2x + 16 = 2(10) + 16 = 36°.
Answer: 36°.