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
x = 4
To solve this problem, we need to use the fact that the angles in a triangle add up to 180 degrees.
m∠RST + m∠RSQ + m∠QST = 180
Since m∠RST = 125°, we can substitute this value into the equation:
125 + m∠RSQ + m∠QST = 180
Now we can simplify the equation:
m∠RSQ + m∠QST = 55
Substituting the given values of m∠RSQ = 4x - 7 and m∠QST = 11x + 12:
4x - 7 + 11x + 12 = 55
Combining like terms:
15x + 5 = 55
Subtracting 5 from both sides:
15x = 50
Dividing both sides by 15:
x = 50/15
Simplifying:
x = 10/3
Therefore, x = 10/3 is the value of x.