Same side interior angles are always supplementary, meaning that the sum of their measures if 180°. So, if one of the same side angles is unknown and written as an expression with a variable, and the other same side angle is give, set their sum equal to 180°. Then, using algebra, solve for the value of the variable. If two same side interior angles are written in expressions of a variable, it is also possible to solve for the value of this variable by taking their sum and setting it equal to 180°. Same side interior angles can be applied to a right trapezoid, for example.
An application of same side interior angles could be this trapezoid here where we have two different variables x and y. Let’s start with the left side here. We see that we have same side interior angles so if I add these add I’ll just write a little plus, I know that I’m going to get 180 degrees, so let’s write an equation. We have 90 plus the same side interior angle which is 3x and we end up with 180. So I’m going to subtract 90 from both sides. All I’m doing right now is solving for x, so 3x equals 90 and it’s pretty easy to see that x must be 30. All I did was divide by 3.
So we’ve solved for x, let’s move over to the right side. Here we have 2 same side interior angles so we know that 3y plus this quantity, 2y minus 10 has to add up to 180 degrees, so if you wanted to, you can write parentheses around this just to assure yourself that I’m adding up these 2 angles and I'm saying that they have to be supplementary.
If I combine like terms I have 5y minus 10 equals 180. Again we’re just solving here I’m going to add 10, 5y equals 190 and next I’m going to divide by 5 and I see that y must be 38 so I’m going to write that up here x is 30, y is 38.The key here same side interior angles are always supplementary.