Question

which measure is of an angle that is coterminal with a 135° angle? 45° 90° 495° 585°

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by the formula \(\theta + 360^{\circ}n\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer).

Step2: Check each option

• For \(n = 1\) and \(\theta=135^{\circ}\), we have \(135^{\circ}+360^{\circ}\times1\).

$$135^{\circ}+ 360^{\circ}=495^{\circ}$$

• For \(45^{\circ}\): If \(135^{\circ}+360^{\circ}n = 45^{\circ}\), then \(360^{\circ}n=45^{\circ}-135^{\circ}=- 90^{\circ}\), and \(n=-\frac{90^{\circ}}{360^{\circ}}=-\frac{1}{4}

otin\mathbb{Z}\).

• For \(90^{\circ}\): If \(135^{\circ}+360^{\circ}n = 90^{\circ}\), then \(360^{\circ}n=90^{\circ}-135^{\circ}=-45^{\circ}\), and \(n =-\frac{45^{\circ}}{360^{\circ}}=-\frac{1}{8}

otin\mathbb{Z}\).

• For \(585^{\circ}\): If \(135^{\circ}+360^{\circ}n = 585^{\circ}\), then \(360^{\circ}n=585^{\circ}-135^{\circ}=450^{\circ}\), and \(n=\frac{450^{\circ}}{360^{\circ}}=\frac{5}{4}

otin\mathbb{Z}\).

Answer:

C. \(495^{\circ}\)