We are given a rhombus shape.
The measure of angle ∠1 = 160°
Recall that in a rhombus, the oppsite angles are equal, this means ∠1 = ∠2
So, ∠2 = 160°
Recall that the sum of all four interior angles in a rhombus must be equal to 360°
The diagonal line divides the angles in half.
This means that angle 3 and angle x are equal.
[tex]\begin{gathered} 160\degree+160\degree+2(\angle3+x)=360\degree_{} \\ 320\degree+2(\angle3+x)=360\degree \\ 2(\angle3+x)=360\degree-320\degree \\ 2(\angle3+x)=40\degree \\ \angle3+x=\frac{40\degree}{2} \\ \angle3+x=20\degree \end{gathered}[/tex]
Since we know that ∠3 and ∠x are equal then
∠3 = 10° and ∠x = 10°
Therefore,
∠2 = 160°
∠3 = 10°
