figure abcd is a parallelogram. what are the measures of angles b and c? ∠b = 15°; ∠c = 165° ∠b = 65°; ∠c =…

Explanation:

Step1: Use property of parallelogram

In a parallelogram, adjacent - angles are supplementary, so $\angle B+\angle C = 180^{\circ}$ and opposite - angles are equal, so $\angle A=\angle C$ and $\angle B=\angle D$. Also, $\angle B=(3n + 20)^{\circ}$ and $\angle D=(6n - 25)^{\circ}$. Since $\angle B=\angle D$ in parallelogram $ABCD$, we set up the equation $3n + 20=6n-25$.

Step2: Solve the equation for $n$

Subtract $3n$ from both sides: $20 = 3n-25$. Then add 25 to both sides: $3n=45$, so $n = 15$.

Step3: Find the measure of $\angle B$

Substitute $n = 15$ into the expression for $\angle B$: $\angle B=(3n + 20)^{\circ}=(3\times15 + 20)^{\circ}=(45 + 20)^{\circ}=65^{\circ}$.

Step4: Find the measure of $\angle C$

Since $\angle B+\angle C = 180^{\circ}$ in parallelogram $ABCD$, then $\angle C=180^{\circ}-\angle B$. Substitute $\angle B = 65^{\circ}$, so $\angle C=180 - 65=115^{\circ}$.

Answer:

$\angle B = 65^{\circ};\angle C = 115^{\circ}$