Question

2)In triangle DEF, mZE is three times mZD, and mZF is 9° less than mZE. What isthe measure of each angle?

Answer 1

`m\angle D=x`
`\begin{gathered} m\angle E=3x \\ \end{gathered}`
`m\angle F=3x-9`

the sum of the angles of a triangle is equal to 180°, then:

`x+3x+3x-9=180`

and solve for x

`\begin{gathered} 7x-9=180 \\ 7x-9+9=180+9 \\ 7x=189 \\ (7x)/(7)=(189)/(7) \\ x=27 \end{gathered}`

therefore the measure of the angles is:

`\begin{gathered} m\angle D=27^(\circ) \\ m\angle E=3(27)=81^(\circ) \\ m\angle F=3(27)-9=72^(\circ) \end{gathered}`