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°.
[tex]m\angle AMB=90[/tex]
Let's find angle ABM using the interior angles theorem on the triangle AMB.
[tex]\begin{gathered} 53+90+m\angle ABM=180 \\ m\angle ABM=180-90-53=37 \end{gathered}[/tex]
Given that diagonals bisect each other, then DM = BM = 6. And, MC = 12.-
Using the tangent function in triangle BMC to find angle MBC
[tex]\begin{gathered} \tan (\angle MBC)=\frac{12}{16} \\ m\angle MBC=\tan ^{-1}(\frac{3}{4})\approx37 \end{gathered}[/tex]
So, using the sum of angles, we have
[tex]m\angle ABC=m\angle ABM+m\angle MBC=37+37=74[/tex]
And the measure of angle DAB is
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