Answer:
mRS = 116
Step-by-step explanation:
If Segment SR ≅ TU then, arc SR ≅ arc TU
Thus, 6x - 28 = 4x + 20
^ ( note that this is the equation we will use to solve for x )
6x - 28 = 4x + 20
step 1 add 28 to each side
28 + -28 cancels out
28 + 20 = 48
we now have 6x = 4x + 48
step 2 subtract 4x from each side
6x - 4x = 2x
4x - 4x cancels out
we now have 2x = 48
step 3 divide each side by 2
2x / 2 = x
48 / 2 = 24
we're left with x = 24
Now to find the value of arc RS we substitute x with 24 in arc RS' given expression
arc RS = 6x - 28
* substitute x with 24 *
arc RS = 6(24) - 28
6 * 24 = 144
144 - 28 = 116
Hence, arc RS = 116
