Question

find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 135° 495°; -45° 315°; -45° 495°; -225° 405°; -135°

Explanation:

Step1: Recall the formula for coterminal angles

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

Step2: Find the positive coterminal angle

Let \(n = 1\), then \(\theta+360^{\circ}=135^{\circ}+ 360^{\circ}=495^{\circ}\).

Step3: Find the negative coterminal angle

Let \(n=-1\), then \(\theta - 360^{\circ}=135^{\circ}-360^{\circ}=-225^{\circ}\).

Answer:

\(495^{\circ};-225^{\circ}\) (the third option)