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
![m\angle A=m\angle C~~~~~\textup{[opposite angles]}\\\\\Rightarrow m\angle 1=128^\circ.](https://img.qammunity.org/2019/formulas/mathematics/high-school/bttt9gcghy5hlmfz8qlajcbg1lnfopv5zi.png)
Also, in ΔBCD, we have
![BC=CD~~\textup{[all the sides are congruent]}\\\\\Rightarrow m\angle 3=m\angle 2~~\textup{[angles opposite to congruent sides care congruent]}.](https://img.qammunity.org/2019/formulas/mathematics/high-school/39cs9e0ms3yz12f744bfc0p9ufm7t1xwkz.png)
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°.