Point Q lies in the interior of ∠RST.
If m∠RST = 125°, m∠RSQ = 4x − 7, m∠QST = 11x + 12, then find x.
diagram
(1 point)
Responses
x = 5
x = 5
x = 8
x = 8
x = 6
x = 6
x = 4
To find x, we need to set up an equation using the information given.
Since Q lies in the interior of ∠RST, we know that the sum of ∠RSQ and ∠QST must be less than 125°.
So, we have the equation:
m∠RSQ + m∠QST < m∠RST
Substituting the given values, we get:
4x - 7 + 11x + 12 < 125
Combining like terms, we have:
15x + 5 < 125
Subtracting 5 from both sides, we get:
15x < 120
Dividing both sides by 15, we get:
x < 8
So, x can be any value less than 8.
Therefore, the correct answer is:
x < 8