josephverde15
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The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.

Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.

Which is correct regarding the angles of the triangle?

mAngleX < mAngleZ < mAngleY

mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX

Respuesta :

frika

Answer:

[tex]m\angle Y<m\angle Z<m\angle X[/tex]

Step-by-step explanation:

In triangle XYZ, the lengths of sides are

  • [tex]XY=m+8;[/tex]
  • [tex]YZ=2m+3;[/tex]
  • [tex]XZ=m-3.[/tex]

If [tex]m\ge 6,[/tex] then

  • [tex]m+8\ge 14;[/tex]
  • [tex]2m+3\ge 15;[/tex]
  • [tex]m-3\ge 3[/tex]

and

[tex]m-3\le m+8\le 2m+3[/tex]

The greatest angle is opposite to the greatest side, the smallest angle is opposite to the smallest side, so

  • the greatest side is [tex]YZ=2m+3[/tex] - the greatest angle is [tex]\angle X;[/tex]
  • the smallest side is [tex]XZ=m-3[/tex] - the smallest angle is [tex]\angle Y.[/tex]

Thus,

[tex]m\angle Y<m\angle Z<m\angle X.[/tex]

Answer:

B

Step-by-step explanation:

mAngleY < mAngleZ < mAngleX

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