Question

I need help finding and reviewing if my answers are correct!

Answer 1

We are looking at the value of x given that m ∠ CDE = x and m ∠ EDF = 3x + 20. We have

`\begin{gathered} m\angle CDE-m\angle EDF=180 \\ x-(3x+20)=180,\mleft(Given\mright) \end{gathered}`

We first apply the distributive property of multiplication over addition on the parenthesis term. We will get

`x-3x-20=180,(\text{Distributive Property of Multiplication over Addition})`

We now simplify the term on the left-hand side since we have x and -3x as like terms. We have

`-2x-20=180,(\text{Simplify})`

Then, we apply the additional property of equality to add 20 on both sides of the equation. We get

`\begin{gathered} -2x-20+20=180+20,(\text{Addition property of equality}) \\ -2x=200,(\text{Simplify}) \end{gathered}`

We now divide both sides by -2 by division property of equality. Hence, we have

`\begin{gathered} (-2x)/(-2)=(200)/(-2),(\text{Division property of equality}) \\ x=-100,() \end{gathered}`

We can summarize the steps as follows

`\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}) \\ (-2x)/(-2)=(200)/(-2),(\text{Division property of equality}) \\ x=-100 \end{gathered}`