Select your answer Which of the angles are coterminal? \( 45^{\circ} \) and \( 225^{\circ} \) \( 30^{\circ} \) and \( -390^{\circ} \) \( 40^{\circ} \) and \( 400^{\circ} \) \( 50^{\circ} \) and \( 420^{\circ} \) \( -60^{\circ} \) and \( -300^{\circ} \)

To determine which pairs of angles are **coterminal**, we need to check if their difference is a multiple of \( 360^\circ \). Two angles are coterminal if they share the same terminal side when positioned in standard position (i.e., their difference is an integer multiple of \( 360^\circ \)). Let's evaluate each pair: 1. **\( 45^\circ \) and \( 225^\circ \)** \[ 225^\circ - 45^\circ = 180^\circ \quad (\text{Not a multiple of } 360^\circ) \] **Not coterminal.** 2. **\( 30^\circ \) and \( -390^\circ \)** \[ -390^\circ + 360^\circ = -30^\circ \\ -30^\circ + 360^\circ = 330^\circ \quad (\text{Difference between } 30^\circ \text{ and } 330^\circ = 300^\circ) \] **Not coterminal.** 3. **\( 40^\circ \) and \( 400^\circ \)** \[ 400^\circ - 40^\circ = 360^\circ \quad (360^\circ \times 1) \] **Coterminal.** 4. **\( 50^\circ \) and \( 420^\circ \)** \[ 420^\circ - 50^\circ = 370^\circ \quad (\text{Not a multiple of } 360^\circ) \] **Not coterminal.** 5. **\( -60^\circ \) and \( -300^\circ \)** \[ -300^\circ - (-60^\circ) = -240^\circ \quad (\text{Not a multiple of } 360^\circ) \] **Not coterminal.** **Conclusion:** Only the pair **\( 40^\circ \) and \( 400^\circ \)** are coterminal. **Answer:** Only 40° and 400° are coterminal.