Find the value of x. The diagram is not to scale.
Given: RS = ST, m<RST = 8x - 60, m<STU = 10x
To find the value of x, we can set up an equation using the fact that the sum of the angle measures in a triangle is 180 degrees.
m<RST + m<STU + m<RUS = 180
We know that m<RST = 8x - 60 and m<STU = 10x. We also know that RS = ST, so m<RUS is equal to m<RST. Thus, we can rewrite the equation as:
8x - 60 + 10x + 8x - 60 = 180
Combining like terms:
26x - 120 = 180
Add 120 to both sides:
26x = 300
Divide both sides by 26:
x = 11.54
Therefore, the value of x is approximately 11.54.