Let's begin by identifying key information given to us:
This is the diagram of a rhombus. A rhombus has the following properties:
I. the opposite angles are congruent
II. the sum of interior angles is 360 degrees
We are given one angle (the angle opposite 1) to be 120 degrees. From the first property listed above, we will see that:
[tex]m\angle1=120^{\circ}[/tex]
Angles 2 & 3 are alternate angles; therefore, they are equal
The sum of angles in a triangle is 180 degrees
We will calculate for angles 2 & 3 thus:
[tex]\begin{gathered} 180-120=2\cdot(m\angle3) \\ 60=2\cdot(m\angle3)\Rightarrow2\cdot(m\angle3)=60 \\ m\angle3=\frac{60}{2}=30 \\ m\angle3=30^{\circ} \\ m\angle3\cong m\angle2=30^{\circ} \end{gathered}[/tex]
