We are looking at the value of x given that m ∠ CDE = x and m ∠ EDF = 3x + 20. We have
[tex]\begin{gathered} m\angle CDE-m\angle EDF=180 \\ x-(3x+20)=180,\mleft(Given\mright) \end{gathered}[/tex]
We first apply the distributive property of multiplication over addition on the parenthesis term. We will get
[tex]x-3x-20=180,(\text{Distributive Property of Multiplication over Addition})[/tex]
We now simplify the term on the left-hand side since we have x and -3x as like terms. We have
[tex]-2x-20=180,(\text{Simplify})[/tex]
Then, we apply the additional property of equality to add 20 on both sides of the equation. We get
[tex]\begin{gathered} -2x-20+20=180+20,(\text{Addition property of equality}) \\ -2x=200,(\text{Simplify}) \end{gathered}[/tex]
We now divide both sides by -2 by division property of equality. Hence, we have
[tex]\begin{gathered} \frac{-2x}{-2}=\frac{200}{-2},(\text{Division property of equality}) \\ x=-100,() \end{gathered}[/tex]
We can summarize the steps as follows
[tex]\begin{gathered} m\angle CDE-m\angle EDF=180 \\ x-(3x+20)=180,(Given) \\ x-3x-20=180,(\text{Distributive Property of Multiplication over Addition}) \\ -2x-20+20=180+20,(\text{Addition property of equality}) \\ \frac{-2x}{-2}=\frac{200}{-2},(\text{Division property of equality}) \\ x=-100 \end{gathered}[/tex]
