Let the measure of $\angle E$ be $x^\text{o}$. How can you write expressions for $m\angle D$ and $m\angle F$ in terms of $x$ using the information given?

Add your expressions for $m\angle D$, $m\angle E$, and $m\angle F$ and set the sum equal to $180$. Solve for $x$, then use that value to find $m\angle D$.

In one expression line, type y1 = 2x + x + (x + 30) to represent the sum of the three angles in terms of $x$ (the measure of $\angle E$).

In the next line, type y2 = 180 to represent the total number of degrees in a triangle.

Look at the graph and tap the intersection point of the two lines $y1$ and $y2$; the $x$-coordinate of this point is the value of $x$, the measure of $\angle E$. Then, in a new expression line, type 2 * (that x-value) to find the measure of $\angle D$ and read the result from Desmos.

Let the measure of $\angle E$ be $x^\text{o}$.

Then, using the given relationships:

• $\angle D$ is twice $\angle E$, so $m\angle D = 2x^\text{o}$.
• $\angle F$ is $30^\text{o}$ more than $\angle E$, so $m\angle F = (x + 30)^\text{o}$.

In any triangle, the three angles add up to $180^\text{o}$.

So for $\triangle DEF$:

Combine like terms:

Solve the equation $4x + 30 = 180$.

Subtract $30$ from both sides:

Divide both sides by $4$:

So $m\angle E = 37.5^\text{o}$.

Angle $D$ is twice angle $E$.

So

Therefore, the measure of $\angle D$ is $75^\text{o}$, which corresponds to choice C.