Let angle $Q$ be $x$ degrees. How can you write angle $P$ in terms of $x$ if it is twice angle $Q$?

Using the fact that angle $R$ is $24^\circ$, write an equation for $x$ based on $\text{angle }P + \text{angle }Q + \text{angle }R = 180$. Then solve for $x$ and use it to find angle $P$.

In a Desmos expression line, type (180 - 24) / 3 and look at the value Desmos gives; this represents the measure of angle $Q$ in degrees.

In a new Desmos line, type 2 * ((180 - 24) / 3) to represent twice angle $Q$. The value Desmos shows is the measure of angle $P$ in degrees; compare this to the answer choices.

We are told that in $\triangle PQR$:

• angle $P$ is twice angle $Q$.
• angle $R$ is $24^\circ$.

Let the measure of angle $Q$ be $x$ degrees. Then the measure of angle $P$ is $2x$ degrees, and angle $R$ is $24^\circ$.

In any triangle, the sum of the three interior angles is $180^\circ$.

So for $\triangle PQR$ we have:

Substitute the expressions in terms of $x$:

Combine like terms on the left:

Subtract 24 from both sides:

Divide both sides by 3:

So angle $Q$ measures $52^\circ$.

Angle $P$ is twice angle $Q$, so its measure is:

So angle $P$ measures $104^\circ$, which corresponds to choice C.