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 = 8
x = 6
x = 4
To solve for x, we can use the fact that the angles in a triangle add up to 180 degrees.
Since ∠RST = 125° and ∠RSQ = 4x - 7, we can write the equation:
125 + (4x - 7) + (11x + 12) = 180
Combine like terms:
15x + 130 = 180
Subtract 130 from both sides:
15x = 50
Divide both sides by 15:
x = 50/15
Simplify:
x = 10/3
So, none of the given options (x = 5, x = 8, x = 6, x = 4) are correct. The correct answer is x = 10/3.