Answer:
m∠E = 69°
Explanation:
Side AB and AC are equal. Let's say they are "x".
We know sum of 3 angles in a triangle is 180. Thus, for Triangle ABC, we can write and solve for x:
x + x + 96 = 180
2x = 180 - 96
2x = 84
x = 84/2
x = 42
Now this angle x and angle C are equal because of vertical angles [angles making a "cross" are vertical angles and are equal].
So Angle C = 42
Now looking at Triangle CDE, we see that CE and CD are equal, so angle opposite are same as well, let's label it "y". Thus we can say for Triangle CDE,
y + y + 42 = 180 [sum of 3 angles in a triangle is 180]
2y + 42 = 180
2y = 180 - 42
2y = 138
y = 138/2
y = 69
This "y" is Angle E, so
m∠E = 69°