In the following diagram it is know that AC≅BC, DE⊥AD, and m∠C=106°. Using this information find m∠E.

Answer:
Angle E is 53 degrees.
Step-by-step explanation:
Let's start with the ABC triangle first.
Since AC=BC, angle A and angle B are equal.
We know that the interior angles of a triangle add up to 180.
106 + A + B = 180
A + B = 74
A = B = 37
Moving on to the BDE triangle.
We have angle B = 37 (it's an opposite angle).
We know that angle D is 90, since this is a right triangle.
90 + 37 + E = 180
E = 53