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

Mya Claims Mlt3 Mlt4 Mlt1 As Shown In The Triangle Below Which Equations Explain Why Myas Claim Must Be True class=

Sagot :

[tex]m\angle1\text{ and m}\angle2\text{ supplementary angles}[/tex]

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

[tex]m\angle1+m\angle2=180^o[/tex]

Using triangle sum property, we get

[tex]\begin{gathered} m\angle2+\angle m3+m\angle4=180^o_{} \\ ^{} \end{gathered}[/tex]

[tex]\text{ Substitute }180^o=m\angle1+m\angle2,\text{ we get}[/tex]

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

[tex]\begin{gathered} m\angle2+\angle m3+m\angle4-m\angle2=m\angle1+m\angle2-m\angle2 \\ ^{} \end{gathered}[/tex]

[tex]\begin{gathered} \angle m3+m\angle4=m\angle1 \\ ^{} \end{gathered}[/tex]

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

[tex]m\angle1+m\angle2=180^o[/tex]

[tex]\begin{gathered} m\angle2+\angle m3+m\angle4=180^o_{} \\ ^{} \end{gathered}[/tex]

Hence the answer is D.

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