Recall the rule that gives that the external angle of a triangle is equal to the sum of the two opposite interior angles. Consider the triangle below:
The rule applies and gives us:
[tex]a+b=c[/tex]
Applying the rule to the question, we have:
[tex](5x+13)\degree=(4x+2)\degree+(2x-9)\degree[/tex]
Solving, we can get x to be:
[tex]\begin{gathered} 5x+13=4x+2+2x-9 \\ 5x+13=4x+2x+2-9 \\ 5x+13=6x-7 \\ 5x-6x=-7-13 \\ -x=-20 \\ \therefore \\ x=20 \end{gathered}[/tex]
The value of x is 20.
