Question

If ∠ABD = 82°, what is ∠ABE?

Answer 1

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

$m\angle ABE=\dfrac{1}{2}\times m\angle ABD=\dfrac{1}{2}\times 82^\circ=41^\circ.$

Thus, the measure of ∠ABE is 41°.

Answer 2

If ∠ABD = 82°,then ∠ABE = 82 /2 = 41

answer:  ∠ABE = 41