Question

which negative angle is equivalent to a 75° angle?
a. an angle measuring -105°
b. an angle measuring -75°
c. an angle measuring -285°
d. an angle measuring -275°

Explanation:

Step1: Recall coterminal angles formula

To find a negative coterminal angle with an angle \( \theta \), we use the formula \( \theta - 360^\circ \) (or \( \theta+ 360^\circ k\), \( k \) is a negative integer for negative coterminal angles). For \( \theta = 75^\circ \), we want to find \( 75^\circ- 360^\circ \).

Step2: Calculate the value

\( 75^\circ- 360^\circ=- 285^\circ \). So the negative angle equivalent to \( 75^\circ \) is \( - 285^\circ \).

Answer:

C. An angle measuring \(-285^\circ\)