Context: Angle $S$ measures $\dfrac{8\pi}{11}$ radians, and angle $T$ measures twice angle $S$. The task is to choose the expression that gives the measure of $T$ in degrees.

Answer: B) $\dfrac{8}{11}(180)(2)$

Why? Doubling gives $T = \dfrac{16\pi}{11}$ radians, and converting to degrees multiplies by $\dfrac{180}{\pi}$, which cancels the $\pi$: $\dfrac{16\pi}{11}\cdot\dfrac{180}{\pi} = \dfrac{8}{11}(180)(2)$.

Traps:

• A) $\dfrac{8}{11}(90)(2)$ uses $90$ where the conversion needs $180$; it collapses to $\dfrac{8}{11}(180)$, which is angle $S$ in degrees, not $T$.
• C) $\dfrac{8}{11\pi}(90)(2)$ divides by $\pi$ instead of cancelling it, so a $\pi$ is left in the denominator and the value is not a degree measure.
• D) $\dfrac{8\pi}{11}(180)(2)$ multiplies the radian measure by $180$ without dividing by $\pi$, leaving an extra factor of $\pi$.