Question

Solve for the measurement of angle E (m

Answer 1

We are given a triangle △DFE

It is given that the sides DF and FE are equal and hence the angles opposite to these sides must also be equal.

So, the angles ∠D and ∠E are equal.

Recall that the sum of all three angles in a triangle must be equal to 180°

`m\angle D+m\angle F+m\angle E=180\degree`

Let us substitute the given values and solve for x

`\begin{gathered} (4x+1)+(5x-4)+(4x+1)=180 \\ 4x+5x+4x+1-4+1=180 \\ 13x-2=180 \\ 13x=180+2 \\ 13x=182 \\ x=(182)/(13) \\ x=14 \end{gathered}`

So, the value of x is 14

Finally, the measure of angle m∠E is

`\begin{gathered} m\angle E=4x+1 \\ m\angle E=4(14)+1 \\ m\angle E=56+1 \\ m\angle E=57\degree \end{gathered}`

Therefore, the measure of m∠E is 57°