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 can write an equation using the angle sum theorem for a triangle.
According to the angle sum theorem, the sum of the angles in a triangle is 180°.
So, in triangle RSQ, we have:
m∠RSQ + m∠QST + m∠RST = 180°
Substituting the given values:
4x - 7 + 11x + 12 + 125° = 180°
Combining like terms:
15x + 130 = 180
Subtracting 130 from both sides:
15x = 50
Dividing both sides by 15:
x = 50/15
Simplifying:
x = 10/3
Therefore, x = 10/3.