Question

In ΔUVW, m, angle, U, equals, left parenthesis, x, minus, 6, right parenthesis, degreesm∠U=(x−6)
∘
, m, angle, V, equals, left parenthesis, 5, x, plus, 6, right parenthesis, degreesm∠V=(5x+6)
∘
, and m, angle, W, equals, left parenthesis, 3, x, plus, 18, right parenthesis, degreesm∠W=(3x+18)
∘
. What is the value of x, question markx?

Answer 1

Sum of angles in a triangle is 180°, so
(x−6)+(5x+6)+(3x+18)=180.
Combine like terms: 9x+18=180 → 9x=162 → x=18.

Check: ∠U=12°, ∠V=96°, ∠W=72°; they sum to 180°. So x = 18.