Question

identify measures of angles that are coterminal with a 145° angle. choose four correct answers. 505° -145° -215° 415° -575° 865° 215° -35°

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by the formula \(\theta + 360n\), where \(\theta = 145^{\circ}\) and \(n\in\mathbb{Z}\) ( \(n\) is an integer).

Step2: Check each angle

• For \(505^{\circ}\):

Let \(n = 1\). Then \(\theta+360n=145 + 360\times1=145 + 360=505^{\circ}\)

• For \(- 215^{\circ}\):

Let \(n=-1\). Then \(\theta + 360n=145+360\times(-1)=145 - 360=-215^{\circ}\)

• For \(-575^{\circ}\):

Let \(n=-2\). Then \(\theta+360n=145+360\times(-2)=145-720=-575^{\circ}\)

• For \(865^{\circ}\):

Let \(n = 2\). Then \(\theta+360n=145+360\times2=145 + 720=865^{\circ}\)

• For \(415^{\circ}\):

\(145+360n = 415\), \(360n=415 - 145=270\), \(n=\frac{270}{360}=\frac{3}{4}
otin\mathbb{Z}\)

• For \(-145^{\circ}\):

\(145+360n=-145\), \(360n=-145 - 145=-290\), \(n=-\frac{290}{360}=-\frac{29}{36}
otin\mathbb{Z}\)

• For \(215^{\circ}\):

\(145+360n = 215\), \(360n=215 - 145 = 70\), \(n=\frac{70}{360}=\frac{7}{36}
otin\mathbb{Z}\)

• For \(-35^{\circ}\):

\(145+360n=-35\), \(360n=-35 - 145=-180\), \(n =-\frac{180}{360}=-\frac{1}{2}
otin\mathbb{Z}\)

Answer:

\(505^{\circ}\), \(-215^{\circ}\), \(-575^{\circ}\), \(865^{\circ}\)