Question

what is m∠n? (4x + 36)° (6x - 2)° a. 19° b. 68° c. 95° d. 112°

Explanation:

Step1: Identify angle - relationship in parallelogram

In a parallelogram, consecutive angles are supplementary, so $\angle M+\angle P = 180^{\circ}$.
$(6x - 2)+(4x + 36)=180$

Step2: Simplify the equation

Combine like - terms:
$6x+4x-2 + 36=180$
$10x+34 = 180$

Step3: Solve for $x$

Subtract 34 from both sides:
$10x=180 - 34$
$10x=146$
$x = 14.6$

Step4: Find $\angle M$

Substitute $x = 14.6$ into the expression for $\angle M$:
$\angle M=6x-2=6\times14.6-2=87.6 - 2=85.6^{\circ}$

Step5: Find $\angle N$

Since $\angle M$ and $\angle N$ are also consecutive angles in a parallelogram, $\angle M+\angle N = 180^{\circ}$.
$\angle N=180-\angle M$
$\angle N=180 - 85.6=94.4\approx95^{\circ}$

Answer:

C. $95^{\circ}$