Let angle $M$ be $x$. Then express angle $L$ and angle $N$ in terms of $x$ using the relationships given in the problem.

Add your expressions for angles $L$, $M$, and $N$, set the sum equal to $180$, and solve the resulting equation for $x$.

After you find $x$ (which represents angle $M$), remember the question is asking for the measure of angle $L$. Use the relationship between angle $L$ and angle $M$ to get the final value.

In Desmos, enter the expression y = 4x + 60 (this represents the sum of the three angle expressions). Then enter y = 180 as a second line (this represents the total degrees in a triangle).

Look at the intersection point of the two lines. The $x$-coordinate of this point is the value of $x$, which is the measure of angle $M$.

Once you know $x$, compute $2x$ (you can type 2*(value) in Desmos) to find the measure of angle $L$, since angle $L$ is twice angle $M$.

Let angle $M$ be $x$ degrees.

• Angle $L$ is twice angle $M$, so angle $L = 2x$.
• Angle $N$ is $60^\circ$ greater than angle $M$, so angle $N = x + 60$.

In any triangle, the three interior angles add up to $180^\circ$.

So for $\triangle LMN$:

Substitute the expressions for each angle in terms of $x$:

First simplify the equation:

Now solve for $x$:

So angle $M$ measures $30^\circ$.

The problem asks for the measure of angle $L$, which is $2x$.

We found $x = 30$, so:

So the measure of angle $L$ is $60^\circ$.