1.) Set up an equation.
All of the angles in a triangle have a sum of 180°. This means that in order to solve this problem, you have to add up all of the angle measures. Since we already know they add up to 180°, then the algebraic equation will look like:
[tex]y + y - 12 + 56 = 180[/tex]
2.) Simplify.
We can see that there are two variables and two known numbers. To make the equation simpler, add up the numbers that are compatible with each other.
[tex](y + y) + (-12 + 56) = 180[/tex]
--> [tex]2y + 44 = 180[/tex]
3.) Isolate y.
If 180 is 44 more than 2y, then that means we can flip this and say that 2y is 44 less than 180. Numerically, this would be:
[tex]2y + 44 = 180[/tex]
--> [tex]2y + 44 - 44 = 180 - 44[/tex]
---> [tex]2y = 136[/tex]
Isolate y using the same concept.
[tex]\frac{2y}{2} = \frac{136}{2}[/tex]
--> [tex]y = \frac{136}{2}[/tex]
We are left with [tex]y = 68[/tex].
4.) Check your work.
Now that we know the value of y, all that's left to do is to plug in the value to see if your answer is true.
[tex](68) + (68) - 12 + 56 = 180[/tex]
--> [tex]136 - 12 + 56 = 180[/tex]
---> [tex]124 + 56 = 180[/tex]
So we know it is true that y = 68°. Hope this was helpful.
