Question

Part 4 out of 6 Statements Reasons 5.mZA +mZB = mZA +mZDE 5. Division Property of Equality

Answer 1

The Part 4 can be written as;

`\begin{gathered} m\angle A+m\angle B=180^(\circ) \\ m\angle A+m\angle D=180^(\circ) \end{gathered}`

Step-by-step explanation:

From part 3;

`\begin{gathered} 2m\angle A+2m\angle B=360^(\circ) \\ 2m\angle A+2m\angle D=360^(\circ) \end{gathered}`

Applying the Division property of equality;

`\begin{gathered} \text{If;} \\ a+b=c \\ \text{then;} \\ (a)/(n)+(b)/(n)=(c)/(n) \end{gathered}`

Divide the equations through by 2;

`\begin{gathered} 2m\angle A+2m\angle B=360^(\circ) \\ (2m\angle A)/(2)+(2m\angle B)/(2)=(360^(\circ))/(2) \\ m\angle A+m\angle B=180^(\circ) \end{gathered}`
`\begin{gathered} 2m\angle A+2m\angle D=360^(\circ) \\ (2m\angle A)/(2)+(2m\angle D)/(2)=(360^(\circ))/(2) \\ m\angle A+m\angle D=180^(\circ) \end{gathered}`

Therefore;

The Part 4 can be written as;

`\begin{gathered} m\angle A+m\angle B=180^(\circ) \\ m\angle A+m\angle D=180^(\circ) \end{gathered}`