figure abcd is a parallelogram. what are the measures of angles b and d? ∠b = 55°; ∠d = 55° ∠b = 55°; ∠d =…

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - angles are equal. So, $\angle B=\angle D$. Also, adjacent angles are supplementary, i.e., $\angle A+\angle B = 180^{\circ}$ and $\angle B+\angle C=180^{\circ}$, $\angle C+\angle D = 180^{\circ}$, $\angle D+\angle A=180^{\circ}$. And $\angle A=(2n + 15)^{\circ}$ and $\angle D=(3n-5)^{\circ}$. Since adjacent angles are supplementary, $\angle A+\angle D=180^{\circ}$. $(2n + 15)+(3n-5)=180$

Step2: Simplify the equation

Combine like - terms: $2n+3n+15 - 5=180$ $5n+10 = 180$ Subtract 10 from both sides: $5n=180 - 10$ $5n=170$ Divide both sides by 5: $n=\frac{170}{5}=34$

Step3: Find the measure of $\angle B$ and $\angle D$

Substitute $n = 34$ into the expression for $\angle B$ (or $\angle D$ since $\angle B=\angle D$). $\angle B=\angle D=(2n + 15)^{\circ}$ $\angle B=\angle D=2\times34 + 15$ $\angle B=\angle D=68+15$ $\angle B=\angle D=83^{\circ}$

Answer:

$\angle B = 83^{\circ};\angle D = 83^{\circ}$ (There seems to be an error in the provided options as the correct answer based on the above - calculation is $\angle B=\angle D = 83^{\circ}$ and none of the given options match exactly. But if we assume there is a mis - typing in the options and we consider the closest concept - related option, we note that in a parallelogram opposite angles are equal. If we had to choose from the given options, we would say there is an issue with the problem setup as the calculated value does not match any of them. But following the steps for a parallelogram's angle - related properties, the correct equal measure for $\angle B$ and $\angle D$ is $83^{\circ}$)