Question

5 multiple choice 6 points
in parallelogram lmno, what is the measure of angle m?
$20^\circ$
$60^\circ$
$80^\circ$
$100^\circ$

Explanation:

Step1: Use parallelogram consecutive angles property

Consecutive angles in a parallelogram are supplementary, so:
$$(3x + 40) + 5x = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$8x + 40 = 180$$
$$8x = 140$$
$$x = \frac{140}{8} = 17.5$$

Step3: Find $\angle N$, then $\angle M$

$\angle N$ and $\angle M$ are supplementary. First calculate $\angle N$:
$$\angle N = 5x = 5\times17.5 = 87.5$$
Then solve for $\angle M$:
$$\angle M = 180 - 87.5 = 92.5$$
*Note: Correcting using alternate property: Opposite angles in parallelogram are equal, consecutive angles are supplementary, so $\angle M = \angle O$, $\angle L = \angle N$. Thus $\angle L + \angle M = 180$, and $\angle L = 3x+40$, $\angle N=5x=\angle L$ (opposite angles equal):
$$3x + 40 = 5x$$
$$2x = 40$$
$$x = 20$$
Now find $\angle L$:
$$\angle L = 3(20)+40 = 100^\circ$$
Then $\angle M = 180 - 100 = 80^\circ$*

Answer:

80° (Option C: 80°)