Question

m∠acn = 11k + 11
m∠aen = 15k - 21
given the parallelogram in the image, solve for m∠acn.
○ m∠acn = 38.5°
○ m∠acn = 66°
○ m∠acn = 54°
○ m∠acn = 99°

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - angles are equal. So $m\angle ACN=m\angle AEN$.
Set up the equation $11k + 11=15k-21$.

Step2: Solve for k

Subtract $11k$ from both sides: $11 = 15k-11k - 21$.
Simplify to get $11 = 4k-21$.
Add 21 to both sides: $11 + 21=4k$, so $32 = 4k$.
Divide both sides by 4: $k=\frac{32}{4}=8$.

Step3: Find $m\angle ACN$

Substitute $k = 8$ into the expression for $m\angle ACN$: $m\angle ACN=11k + 11$.
$m\angle ACN=11\times8 + 11=88 + 11=66^{\circ}$.

Answer:

$m\angle ACN = 66^{\circ}$