Question

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

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Answer 1

Angle E is 53 degrees.

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