Answer: The measure of ∠ABE is 41°.
Step-by-step explanation: We are given that ∠ABD = 82°.
We are to find the measure of ∠ABE.
From the figure, we note that
ABDC is a kite with diagonals AD and BC intersecting at the point E. The diagonal BC is the main diagonal of the kite.
We know that
the main diagonal of a kite bisects the pair of opposite angles.
That is, the diagonal BC bisects ∠ABD.
So, we have
[tex]m\angle ABE=\dfrac{1}{2}\times m\angle ABD=\dfrac{1}{2}\times 82^\circ=41^\circ.[/tex]
Thus, the measure of ∠ABE is 41°.
