Question

homework question 3, for thought t/f-1.1.7 hw score: 13.33%, 2 o points: 0 of 1 determine whether the following statement is true or false. explain. angles of 60° and 410° are coterminal. choose the correct answer below. a. the statement is false because degree measures of coterminal angles differ by a multiple of 360° and 410° - 360° = 50°. b. the statement is false because degree measures of coterminal angles differ by a multiple of 180° and 410° - 180° = 230°. c. the statement is true because degree measures of coterminal angles differ by a multiple of 350° and 410° - 350° = 60°. d. the statement is true because degree measures of coterminal angles differ by a multiple of 180° and 410° - 2·180° = 60°.

Explanation:

To determine if two angles are coterminal, their degree measures should differ by a multiple of \(360^\circ\) (for angles in standard position, coterminal angles are obtained by adding or subtracting \(360^\circ\) repeatedly).

• For \(60^\circ\) and \(410^\circ\): Calculate the difference \(410^\circ - 360^\circ = 50^\circ\), not \(60^\circ\). So they are not coterminal.
• Option A correctly states that coterminal angles differ by a multiple of \(360^\circ\) and shows \(410^\circ - 360^\circ = 50^\circ\), not \(60^\circ\), so the statement is false.
• Option B is wrong because coterminal angles differ by multiples of \(360^\circ\), not \(180^\circ\) ( \(180^\circ\) relates to supplementary or reference angles in some cases, not coterminal).
• Options C and D are wrong as they use incorrect multiples (\(350^\circ\) or \(180^\circ\)) for coterminal angle differences.

Answer:

A. The statement is false because degree measures of coterminal angles differ by a multiple of \(360^\circ\) and \(410^\circ - 360^\circ = 50^\circ\).