Question

what is the measure of angle l in parallelogram lmno?
options: 20°, 30°, 40°, 50°
figure: parallelogram lmno with angle at n labeled (2x)° and angle at l labeled (3x - 20)°

Explanation:

Step1: Use parallelogram consecutive angles property

Consecutive angles in a parallelogram are supplementary, so:
$$2x + (3x - 20) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$5x - 20 = 180$$
$$5x = 200$$
$$x = 40$$

Step3: Find angle $L$ measure

Angle $L$ is equal to angle $N$ (opposite angles in a parallelogram are congruent):
$$\text{Angle } L = 2x = 2(40) = 80$$
Wait, correction: Angle $L$ is labeled as $(3x-20)^\circ$, substitute $x=40$:
$$\text{Angle } L = 3(40) - 20 = 120 - 20 = 100$$
Wait, no—correction: Consecutive angles are $\angle N$ and $\angle L$? No, in parallelogram $LMNO$, $\angle N$ and $\angle L$ are opposite angles, so they are congruent. Consecutive angles are $\angle N$ and $\angle M$, $\angle N$ and $\angle O$. So correct property: Opposite angles are equal, so $\angle L = \angle N$? No, no—$LMNO$ vertices are in order, so sides $LM \parallel ON$, $LO \parallel MN$. So $\angle N$ and $\angle L$ are consecutive angles (connected by side $LN$? No, vertices are $L, M, N, O$: so angles $\angle L$ is at vertex $L$, adjacent to $\angle M$ and $\angle O$. $\angle N$ is opposite $\angle L$. So opposite angles are equal: $\angle L = \angle N$, $\angle M = \angle O$. Consecutive angles sum to 180: $\angle L + \angle M = 180$, $\angle N + \angle O = 180$.

Wait, the diagram shows $\angle N = 2x$, $\angle L = 3x-20$. Since they are opposite angles, they are equal:
$$3x - 20 = 2x$$
$$3x - 2x = 20$$
$$x = 20$$
Then $\angle L = 3(20) - 20 = 60 - 20 = 40^\circ$

This matches the options. My earlier mistake was misidentifying consecutive angles. Correct: in labeled parallelogram $LMNO$, the order is $L-M-N-O-L$, so $\angle L$ is opposite $\angle N$, so they are congruent.

Step1: Set opposite angles equal

In parallelogram, opposite angles are congruent:
$$3x - 20 = 2x$$

Step2: Solve for $x$

Isolate $x$:
$$3x - 2x = 20$$
$$x = 20$$

Step3: Calculate angle $L$

Substitute $x$ into angle $L$ expression:
$$\angle L = 3(20) - 20 = 40$$

Answer:

B. 40°