Question

figure abcd is a parallelogram. what is the value of n? (2n + 32)° (4n - 2)° o 3 o 5 o 17 o 25

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, opposite angles are equal. So, $\angle A=\angle C$ and $\angle B=\angle D$. Here, $\angle B=(2n + 32)^{\circ}$ and $\angle D=(4n-2)^{\circ}$, and since $\angle B=\angle D$ in parallelogram $ABCD$, we set up the equation $2n + 32=4n-2$.

Step2: Solve the equation for $n$

First, subtract $2n$ from both sides: $32=4n - 2-2n$, which simplifies to $32 = 2n-2$. Then add 2 to both sides: $32 + 2=2n$, so $34 = 2n$. Divide both sides by 2: $n=\frac{34}{2}=17$.

Answer:

$17$