Question

which of the following angles is not coterminal with the other three?
441°
99°
-279°
81°
6
multiple choice 1 point
which of the following angles is not coterminal with the other three?
79°
-259°
461°
101°

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are angles that can be written in the form \(\theta + n\times360^{\circ}\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer).

Step2: Check each angle for the first set

• For \(441^{\circ}\): \(441^{\circ}- 360^{\circ}=81^{\circ}\)
• For \(- 279^{\circ}\): \(-279^{\circ}+360^{\circ}=81^{\circ}\)
• \(99^{\circ}\) cannot be written as \(81^{\circ}+n\times360^{\circ}\) for any integer \(n\)
• \(81^{\circ}\) is itself.

Step3: Check each angle for the second set

• For \(-259^{\circ}\): \(-259^{\circ}+360^{\circ} = 101^{\circ}\)
• For \(461^{\circ}\): \(461^{\circ}-360^{\circ}=101^{\circ}\)
• \(79^{\circ}\) cannot be written as \(101^{\circ}+n\times360^{\circ}\) for any integer \(n\)
• \(101^{\circ}\) is itself.

Answer:

First set: \(99^{\circ}\)
Second set: \(79^{\circ}\)