The first step that we must take before attempting to solve almost any problem is to determine what the problem statement is asking us to do and what they are giving to us to help finish the problem. Looking at this question we can see that they have requested for us to solve for x and we were provided with a figure.
After understanding what the problem is asking for us to do we can attempt to solve the problem. We can see that there are two angles on a straight line and this is known as supplementary angles. Let us define what supplementary angles are.
- Supplementary Angles ⇒ Supplementary Angles are two angles that are formed on a straight line causing them to add up to 180 degrees. Therefore, an expression can be made where the two angles add up to 180 and it can be solved for the unknown.
In this case we don't have a missing angle but rather a variable that makes up each of the angles. Using a similar concept we can create an expression with 4x - 6 and 2x and have them combined to equal to 180. After that we can solve for the unknown which in turn would give us x.
Create an expression
Combine like terms
Add 6 to both sides
Divide both sides by 6
Therefore, after creating an expression and then simplifying it down all the way to just have the value of x equal to something we were able to determine that the unknown variable of x is equal to 31.