The problem says $m\angle B$ is twice $m\angle A$. How can you write $m\angle B$ in terms of $m\angle A$?

Once $m\angle B$ is written in terms of $m\angle A$, substitute $m\angle A = 35^\circ$ to find $m\angle B$.

Now that you know $m\angle A$ and $m\angle B$, use the fact that the three angles add to $180^\circ$ to solve for $m\angle C$.

In the Desmos calculator, type the expression 180 - (35 + 2*35) and press Enter. The value that Desmos outputs is the measure of $\angle C$ in degrees.

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

We will use this relationship to solve for $m\angle C$.

The problem says $m\angle B$ is twice $m\angle A$.

Since $m\angle A = 35^\circ$:

Now we know two angles: $m\angle A = 35^\circ$ and $m\angle B = 70^\circ$.

Substitute the known angle measures into the triangle angle sum equation:

Combine the known angles:

Subtract $105^\circ$ from $180^\circ$ to isolate $m\angle C$:

So the measure of $\angle C$ is $75^\circ$, which corresponds to choice C.