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

Explanation:

Step1: Recall property of parallelogram

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

Step2: Solve the equation for n

Subtract $2n$ from both sides: $2n+15-2n=3n - 5-2n$ $15=n - 5$ Add 5 to both sides: $15 + 5=n-5 + 5$ $n = 20$

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

Substitute $n = 20$ into the expression for $\angle B$ (or $\angle D$ since they are equal). $\angle B=2n + 15=2\times20+15=40 + 15=55^{\circ}$ $\angle D=3n - 5=3\times20-5=60 - 5=55^{\circ}$

Answer:

$\angle B = 55^{\circ};\angle D = 55^{\circ}$