Question

I need help filling in the reasoning that justifies each step

Answer 1

Since angleCDE is equal to x and angleEDF is 3x+20, we have

`x-(3x+20)=180`

Now, by distributing the minus sign into the parenthesis (Distributive property) we have

`x-3x-20=180`

By combining similar terms (Addition property), we get

`-2x-20=180`

By adding 20 to both sides (Inverse property of addition), we obtain

`\begin{gathered} -2x-20+20=180+20 \\ \text{then} \\ -2x=200 \end{gathered}`

Finally, by multiplying both side by -1/2 (Inverse property of Multiplication), we get

`\begin{gathered} (-(1)/(2))*-2x=-(1)/(2)*200 \\ (-2)/(-2)x=-100 \\ x=-100 \end{gathered}`

Then, x is equal to -100