Question

Mya claims [m<3 + m<4= m<1, as shown in the triangle below. Which equations explain why Mya's claim must be true?

Answer 1

`m\angle1\text{ and m}\angle2\text{ supplementary angles}`

We know that the sum of supplementary angels is 180 degrees.

`m\angle1+m\angle2=180^o`

Using triangle sum property, we get

`\begin{gathered} m\angle2+\angle m3+m\angle4=180^o_{} \\ ^{} \end{gathered}`

`\text{ Substitute }180^o=m\angle1+m\angle2,\text{ we get}`

`\begin{gathered} m\angle2+\angle m3+m\angle4=m\angle1+m\angle2 \\ ^{} \end{gathered}`
`\text{ Subtracting m}\angle2\text{ from both sides, we get}`

`\begin{gathered} m\angle2+\angle m3+m\angle4-m\angle2=m\angle1+m\angle2-m\angle2 \\ ^{} \end{gathered}`

`\begin{gathered} \angle m3+m\angle4=m\angle1 \\ ^{} \end{gathered}`

We get results by using the following equations. Mia's claim must be true from the following equations.

`m\angle1+m\angle2=180^o`

`\begin{gathered} m\angle2+\angle m3+m\angle4=180^o_{} \\ ^{} \end{gathered}`

Hence the answer is D.