Question

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

Answer 1

B

Explanation:

mAngleY < mAngleZ < mAngleX

Answer 2

`m\angle Y<m\angle Z<m\angle X`

Explanation:

In triangle XYZ, the lengths of sides are

• 
  `XY=m+8;`
• 
  `YZ=2m+3;`
• 
  `XZ=m-3.`

If
`m\ge 6,` then

• 
  `m+8\ge 14;`
• 
  `2m+3\ge 15;`
• 
  `m-3\ge 3`

and

`m-3\le m+8\le 2m+3`

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

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

Thus,

`m\angle Y<m\angle Z<m\angle X.`