To find the measure of the angle ∠ DAB, we first need to find the value of x.
Recall that consecutive angles in a parallelogram are supplementary. This means that the measures of ∠ ABC and ∠ BCD add up to 180.
m ∠ ABC+ m ∠ BCD = 180We are given that m ∠ ABC =2x-7 and m ∠ BCD = 2x+3. We can substitute these expressions into our equation.
2x-7+2x+3 = 180
Now we can solve this equation for x.
Notice that ∠ DAB is opposite to ∠ BCD. Since a rhombus is a parallelogram, its opposite angles are congruent. This means that their measures are equal.
m ∠ DAB = m ∠ BCD
We already know that m ∠ BCD =2x+3. Substituting this into the above equation, we get that m ∠ DAB= 2x+3 as well. Finally, we can substitute x=46 into this equation to find the measure of the angle.
