Acircle is divided into three arcs in the ratio of 3: 4: 5. find the measure of an inscribed angle that intercepts the largest arc.

If the ratio is 3:4:5 it's good to know what the ratio of one of those three to the total is.
3+4+5 = 12.
So the "3" in 3:4:5 is actually 3/12th of a circle (that's 1/4th, a quarter!).
What about the largest part?
The "5" in 3:4:5 is actually 5/12th of a circle!

We know a circle has a total of 360 degrees.
We need 5/12th of that.
So we mulitply: 360 * 5/12 = 150 degrees.

Zero is the mid point of the line segment