Question

m∠eac = 16r - 11
m∠acn = 12r + 23
given the parallelogram in the image, solve for r.
cannot solve for the variable with this information
r = 6
r = 8.5
r = 5

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, opposite - angles are equal or alternate interior angles are equal. $\angle EAC$ and $\angle ACN$ are alternate interior angles. So, $m\angle EAC=m\angle ACN$.

Step2: Set up the equation

$16r - 11=12r + 23$.

Step3: Solve for $r$

Subtract $12r$ from both sides: $16r-12r - 11=12r-12r + 23$, which simplifies to $4r-11 = 23$. Then add 11 to both sides: $4r-11 + 11=23 + 11$, getting $4r=34$. Divide both sides by 4: $r=\frac{34}{4}=8.5$.

Answer:

B. $r = 8.5$