Question

In the rhombus m<1 = 160 what are m<2 and m<3. This diagram is not drawn to scale. Show all work

Answer 1

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.

`\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=(40\degree)/(2) \\ \angle3+x=20\degree \end{gathered}`

Since we know that ∠3 and ∠x are equal then

∠3 = 10° and ∠x = 10°

Therefore,

∠2 = 160°

∠3 = 10°