How do I find angle CAE?

Explanation:

Angle DAB and angle ABC are congruent angles due to the parallel lines (note they are alternate interior angles).

So angle DAB = 47 since angle ABC = 47.

Let angle CAE be equal to x for now.  

The three angles DAB, CAB, and CAE all add up and combine to form a straight angle which is 180 degrees.

We'll use this fact to find x

(angle DAB) + (angle CAB) + (angle CAE) = 180

(47) + (105) + (x) = 180

x + 152 = 180

x + 152-152 = 180-152 subtract 152 from both sides

x = 28

angle CAE = 28 degrees

∠cbe and ∠deb are same-side interior angles.

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