Point Q lies in the interior of ∠RST.
If m∠RST = 125°, m∠RSQ = 4x − 7, m∠QST = 11x + 12, then find x.
Since Q lies in the interior of ∠RST, we know that the sum of ∠RSQ and ∠QST must be less than 180°.
Therefore, we have the following inequality:
m∠RSQ + m∠QST < 180°
Substituting the given expressions for m∠RSQ and m∠QST, we have:
(4x - 7) + (11x + 12) < 180°
Combining like terms, we get:
15x + 5 < 180°
Subtracting 5 from both sides of the inequality, we get:
15x < 175°
Dividing both sides by 15, we get:
x < 11.666...
Since x represents an angle measure and must be a whole number, the largest possible value of x is 11.
Therefore, x < 11.