Answer: m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.
Step-by-step explanation: We are given to find the measures of ∠1, ∠2 and ∠3 in the figure.
As shown in the attached figure, ABCD is a rhombus, where m∠A = 128°.
We know that, in a rhombus, all the sides are congruent, the opposite angles are congruent and the adjacent angles are supplementary.
So, from rhombus ABCD, we have
Also, in ΔBCD, we have
Now, since the sum of three angles of a triangle is 180°, we have from ΔBCD that
Therefore, m∠3 = 26°.
Thus, m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.