Select all that are measures of angles coterminal with a 145° angle. –575° –215° –145° –35° 215° 415° 505° 865°

ANSWER
[tex]- 575 \degree, - 215 \degree,505 \degree,865\degree[/tex]

EXPLANATION

Coterminal angles are two or more angles in standard position that have the same terminal side.

To find angles that are coterminal with [tex]145 \degree[/tex], we keep adding or subtracting multiples of [tex]360\degree[/tex]

Let us add first to get,

[tex]145 \degree + 360 \degree = 505 \degree[/tex]

We add again to get,

[tex]145 \degree + 2(360) \degree = 865\degree[/tex]

Since we reached the highest angle among the options we now subtract.

[tex]145 \degree - 360 \degree = - 215 \degree[/tex]

We subtract the next multiple to get,

[tex]145 \degree - 2( 360 \degree )= - 575\degree[/tex]

This is also the least among the options.

Therefore the angles that are coterminal with 145° are,

[tex] - 575 \degree, - 215 \degree,505 \degree,865\degree[/tex]