Question

Another geometry problem!

Answer 1

The triangle is isosceles with  vertex angle =  116 
So m < E  = (180 - 116) / 2 = 32 degrees

Answer 2

Comment

Fact One
You are given 1 angle which is enclosed by 2 equal sides. That means you have an isosceles triangle. The angles opposite the equal sides are equal.

Fact Two
Every triangle has 180°

Step One
Set up the equation using fact one above.
2 equal angles + 116 = 180
2x + 116 = 180

Step Two
Solve the equation
2x + 116 = 180           Subtract 116 from both sides.
2x = 180 - 116
2x = 64                      Divide by 2
x = 64/2
x = 32

Conclusion
Each of the equal angles = 32°

E = 32° <<<<< answer