Answer:
Hello! I'm here to help you with your question. To start, I'll need to clarify that the equation you provided, m <1 = 7x + 7, is not a correct mathematical expression. The symbol "<" is not a valid mathematical operator, and the equation does not make sense.
However, if you meant to ask for the value of x in the equation 7x + 7 = m, where m is an angle bisector of ∠PT, then we can solve for x using basic trigonometry.
First, let's draw a diagram of the situation:
In this diagram, we can see that ∠PT is an angle bisected by the line m. This means that the angle ∠PT is equal to half of its supplementary angle, which is ∠QTR.
Using the trigonometric identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we can find the length of the side opposite angle ∠PT:
sin(∠PT) = sin(∠QTR / 2)
Now, we can use the fact that sin(∠QTR / 2) = 7x + 7 to find the value of x:
7x + 7 = sin(∠PT)
Simplifying the equation, we get:
7x + 7 = sin(∠QTR / 2)
Solving for x, we get:
x = (7 / 2)sin(∠QTR / 2)
Therefore, the value of x is:
x = 7 / 2sin(∠QTR / 2)
Explanation: