Question

figure abcd is a parallelogram.
what are the measures of angles b and c?
∠b = 15°; ∠c = 165°
∠b = 65°; ∠c = 115°
∠b = 65°; ∠c = 65°
∠b = 15°; ∠c = 15°

Explanation:

Step1: Set equal congruent angles

In a parallelogram, opposite angles are equal, so $\angle B = \angle D$.
$3n + 20 = 6n - 25$

Step2: Solve for n

Rearrange to isolate n:
$20 + 25 = 6n - 3n$
$45 = 3n$
$n = \frac{45}{3} = 15$

Step3: Calculate $\angle B$

Substitute n=15 into $\angle B$:
$\angle B = 3(15) + 20 = 45 + 20 = 65^\circ$

Step4: Calculate $\angle C$

Consecutive angles in a parallelogram are supplementary:
$\angle B + \angle C = 180^\circ$
$\angle C = 180^\circ - 65^\circ = 115^\circ$

Answer:

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