Answer:
mRS = 110
Step-by-step explanation:
Since RS and TU have the same length, we can say that the arc formed by these segments has the same measure. So, we can write the following equation:
4x + 18 = 7x - 51
Now, we can solve the equation for x, so add 52 to both sides:
4x + 18 + 51 = 7x - 51 + 51
4x + 69 = 7x
Subtract 4x from both sides:
4x + 69 - 4x = 7x - 4x
69 = 3x
Finally, divide both sides by 3:
69/3 = 3x/3
23 = x
Now, we can substitute x = 23 on the arc formed by points R and S.
4x + 18 = 4(23) + 18
4x + 18 = 92 + 18
4x + 18 = 110
Therefore, the measure of arc RS is 110
mRS = 110