Question

find the angle of the least positive measure (in degrees, not equal to the given measure) that is coterminal with a. a = -486° the measure is ☐°.

Explanation:

Step1: Recall coterminal angle formula

To find a coterminal angle with a given angle \( \theta \) in degrees, we use the formula \( \theta + 360^{\circ} \times n \), where \( n \) is an integer. We need to find the smallest positive \( n \) such that \( \theta + 360^{\circ} \times n>0 \). Given \( \theta=- 486^{\circ} \).

Step2: Find the appropriate n

Let's solve \( - 486^{\circ}+360^{\circ}\times n>0 \) for \( n \).
\( 360^{\circ}\times n>486^{\circ} \)
\( n >\frac{486^{\circ}}{360^{\circ}}=\frac{27}{20} = 1.35 \)
Since \( n \) is an integer, the smallest integer \( n \) satisfying this is \( n = 2 \).

Step3: Calculate the coterminal angle

Substitute \( n = 2 \) into the formula:
\( -486^{\circ}+360^{\circ}\times2=-486^{\circ} + 720^{\circ}=234^{\circ} \)

Answer:

\( 234 \)