# How do you find the radian measure of an angle of 110?

You need to use a conversion ratio: ## 1 pi ## radians to 180 degrees, getting ##(11 pi) / 18##.
As with all conversions, you need to set up a proportion. Proportions are two ratios set equal to each other. When making the proportions, make sure you line everything up. That means, if you put one measurement over the other, do the same on the other side. Don’t flip the order.
For example, let’s say that you have to convert 4 feet to inches. You know that the conversion ratio is 12 inches to 1 foot. With this information, you want to set up your ratio. For this example, let’s put inches on top and feet on the bottom, giving you:
## (i.nches) / (feet) = (i.nches) / (feet)## (sorry for the i.nches, but this program will read in as something else)
Start with your conversion ratio on the left. You should get: ## (12 i.n) / (1 ft)##.
Now, on the right side, put what you know for feet and a variable (x) for what you are trying to find: ## (x i.n) / (4 ft)##.
Let’s put it together, cross-multiply and solve! (for the sake of the inches not coming out, I am now going to drop my measurements — something that I would not do on paper).
## 12/1 = x/4##
##4 * 12 = 1 * x##
##48 = x##
So 48 inches = 4 feet.
Now converting to degree from radian or vice-versa is not that hard. You can follow the same process.
On the left: ##(1 pi) / 180##.
On the right: ## x / 110 ##
Set them equal to each other, cross-multiply and solve.
## (1 pi) / 180 = x / 110##
## 110 * (1 pi) = 180 * x##
## 110 pi = 180x ##
##(110 pi) / 180 = x##
## (11 pi) / 18 = x##
Note that the final answer is a reduced fraction without actually calculating ##pi## into it. Fractions are more accurate than decimals, so try not to round. Besides, it’s good practice in working with these fraction. You will use them all time (## (3 pi) / 2, (pi)/2, …##)!

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