Step 1
Properties of a Rhombus
Below are some important facts about the rhombus angles:
Rhombus has four interior angles.
The sum of interior angles of a rhombus add up to 360 degrees.
The opposite angles of a rhombus are equal to each other.
The adjacent angles are supplementary.
In a rhombus, diagonals bisect each other at right angles.
The diagonals of a rhombus bisect these angles.
Step 2
From the figure
Angle DGF = Angle DEF = 118
Step 3
Since adjacent angles are supplementary, that is add to 180 degrees
[tex]\begin{gathered} \angle\text{DGF + }\angle GFE\text{ = 180} \\ 118\text{ + }\angle GFE\text{ = 180} \\ \angle GFE\text{ = 180 - 118} \\ \angle GFE\text{ = 62} \end{gathered}[/tex]
Step 4
The diagonals of a rhombus bisect these angles
[tex]\begin{gathered} \angle3\text{ = }\angle4\text{ = }\frac{62}{2}\text{ = 31} \\ \angle3\text{ = }\angle4\text{ = 31} \end{gathered}[/tex]
Step 5
The opposite angles of a rhombus are equal to each other.
[tex]\angle1\text{ = }\angle\text{ 2 = 31}[/tex]
Final answer
[tex]\angle\text{1 = }\angle\text{ 2 = }\angle\text{ 3 = }\angle4\text{ = 31}[/tex]
