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$In /_\DEF,mDE=8 inches, mEF=6 inches, and mDF=10 inches. Which lists the angles in order from smallest to largest ? /_F,/_D,/_E /_D,/_F,/_E /_E,/_F,/_D /_D,/_E,/_F Option 1 Option 2 Option 3 Option 4$

In $\triangle D E F, \mathrm{~m} D E=8$ inches, $\mathrm{m} E F=6$ inches, and $m D F=10$ inches. Which lists the angles in order from smallest to largest ? $\newline$ $\angle F, \angle D, \angle E$ $\newline$ $\angle D, \angle F, \angle E$ $\newline$ $\angle E, \angle F, \angle D$ $\newline$ $\angle D, \angle E, \angle F$ $\newline$ Option $1$ $\newline$ Option $2$ $\newline$ Option $3$ $\newline$ Option $4$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. In

\triangle D E F, \mathrm{~m} D E=8

inches,

\mathrm{m} E F=6

inches, and

m D F=10

inches. Which lists the angles in order from smallest to largest ?

\newline

\angle F, \angle D, \angle E

\newline

\angle D, \angle F, \angle E

\newline

\angle E, \angle F, \angle D

\newline

\angle D, \angle E, \angle F

\newline

Option

1

\newline

Option

2

\newline

Option

3

\newline

Option

4

Identify longest side: Identify the longest side of the triangle to determine the largest angle, using the triangle inequality theorem.
Determine largest angle: According to the triangle inequality theorem, the angle opposite the longest side is the largest. Therefore, angle $E$ is the largest.
Compare remaining sides: Next, compare the remaining sides to order the smaller angles. Since $mEF$ ( $6$ inches) is shorter than $mDE$ ( $8$ inches), angle $D$ is smaller than angle $F$ .
List angles in order: List the angles in order from smallest to largest: $\angle D$ , $\angle F$ , $\angle E$ .

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