The difference between the measure of angle A and the measure of angle B is -5/12 π radians. Which expression shows the difference between the measure of angle A and the measure of angle B, in degrees?

The difference between the measure of angle A and the measure of angle B is -5/12 π... | SAT Right triangles and trigonometry Practice

Context: The difference between the angle measures is $-\dfrac{5}{12}\pi$ radians, and we need the expression that converts this measure to degrees.

Answer: C) $-\dfrac{5}{12}\pi \cdot \dfrac{180^\circ}{\pi}$

Why: Since $\pi$ radians $= 180^\circ$ , converting radians to degrees means multiplying by $\dfrac{180^\circ}{\pi}$ . Applying it to the given measure: $-\dfrac{5}{12}\pi \cdot \dfrac{180^\circ}{\pi} = -\dfrac{5}{12}(180^\circ) = -75^\circ$ .

Traps:

A) drops the $\pi$ from the angle itself: the quantity being converted must be $-\dfrac{5}{12}\pi$ , not $-\dfrac{5}{12}$
B) multiplies by $\dfrac{\pi}{180^\circ}$ , the degrees-to-radians factor, converting in the wrong direction
D) uses $\dfrac{360^\circ}{\pi}$ ; $\pi$ radians equals $180^\circ$ , not $360^\circ$

Question Bank

Question Bank

SAT Right triangles and trigonometry practice question

Explanation