Point Q lies in the interior of ∠RST. If m∠RST = 125°, m∠RSQ = 4x − 7, m∠QST = 11x + 12, then find x. (1 point) Responses x = 5 x = 5 x = 8 x = 8 x = 6 x = 6 x = 4
m∠RST + m∠RSQ + m∠QST = 180° (angle sum of a triangle)
125° + (4x - 7)° + (11x + 12)° = 180°
Combine like terms:
4x + 11x + 125 + 12 = 180
15x + 137 = 180
Subtract 137 from both sides of the equation:
15x = 180 - 137
15x = 43
Divide both sides by 15:
x = 43/15
x = 2 13/15 or 2.8666667
So, the value of x is approximately 2.87