Question

Question 2 This is a rhombus. Using it's properties, what is the measure of it by using the numbers: 120° ( and it has 1, 2, 3, for the number of angles) Special Parallelograms. I need to find the 3 angles

Answer 1

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:

`m\angle1=120^(\circ)`

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:

`\begin{gathered} 180-120=2\cdot(m\angle3) \\ 60=2\cdot(m\angle3)\Rightarrow2\cdot(m\angle3)=60 \\ m\angle3=(60)/(2)=30 \\ m\angle3=30^(\circ) \\ m\angle3\cong m\angle2=30^(\circ) \end{gathered}`