Question

Given the following rhombus ABCD, find measure of angle DAB, ABC, AMB. Also find DM! :)

Answer 1

We know that diagonals bisect the angles because the figure is a rhombus. Also, the diagonals bisect each other at right angles.

We can find AMB using the diagonal property because AMB is a right angle, that is, it's equal to 90°.

`m\angle AMB=90`

Let's find angle ABM using the interior angles theorem on the triangle AMB.

`\begin{gathered} 53+90+m\angle ABM=180 \\ m\angle ABM=180-90-53=37 \end{gathered}`

Given that diagonals bisect each other, then DM = BM = 6. And, MC = 12.-

Using the tangent function in triangle BMC to find angle MBC

`\begin{gathered} \tan (\angle MBC)=(12)/(16) \\ m\angle MBC=\tan ^(-1)((3)/(4))\approx37 \end{gathered}`

So, using the sum of angles, we have

`m\angle ABC=m\angle ABM+m\angle MBC=37+37=74`

And the measure of angle DAB is