What is the measure of e, in degrees

The correct answer is 84º.

Explanation:

The triangle presented is an isosceles triangle and we can determine this because we were given the measurements of two of its sides, and these are exactly the same.

The ED side measures 5 and the EF side also measures 5.

Now let's see, we only have the measure of one of its angles. The angle D with 48º.

But by definition, an angle that is opposite the sides whose measurements are equal must measure exactly the same.

Therefore, we already know that angle F will also measure 48º.

Having two of the angles measured, we only need to find the measure of the angle E. And for that we have to remember that all the internal angles of a triangle add up to a total of 180º, therefore you just have to make a difference:

D + F + E = 180º

48º 48º + E = 180º

E = 180º - 48º - 48º

E = 84º

The correct answer is 84º.