Question

which expression finds the measure of an angle that is coterminal with a 126° angle? 126° + (275n)°, for any integer n 126° + (375n)°, for any integer n 126° + (450n)°, for any integer n 126° + (720n)°, for any integer n

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are angles that have the same initial and terminal sides. The formula for finding coterminal angles of an angle \(\theta\) is \(\theta+(360n)^{\circ}\), where \(n\) is any integer. Since \(720 = 2\times360\), angles of the form \(\theta+(720n)^{\circ}\) (because \(720n = 360\times(2n)\) and \(2n\) is also an integer when \(n\) is an integer) will also be coterminal with \(\theta\).

Step2: Check each option

• For the option \(126^{\circ}+(275n)^{\circ}\): \(275\) is not a multiple of \(360\).
• For the option \(126^{\circ}+(375n)^{\circ}\): \(375\) is not a multiple of \(360\).
• For the option \(126^{\circ}+(450n)^{\circ}\): \(450\) is not a multiple of \(360\).
• For the option \(126^{\circ}+(720n)^{\circ}\): Since \(720 = 2\times360\), when \(n\) is an integer, \(720n\) represents a full - rotation (or multiple full - rotations) around the coordinate plane.

Answer:

\(126^{\circ}+(720n)^{\circ}\), for any integer \(n\) (the fourth option).