Question

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

Answer 1

Let us add first to get,

145 \degree + 360 \degree = 505 \degree145°+360°=505°

We add again to get,

145 \degree + 2(360) \degree = 865\degree145°+2(360)°=865°

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

145 \degree - 360 \degree = - 215 \degree145°−360°=−215°

We subtract the next multiple to get,

145 \degree - 2( 360 \degree )= - 575\degree145°−2(360°)=−575°

This is also the least among the options.

Therefore the angles that are coterminal with 145° are,

-

Answer 2

ANSWER

`- 575 \degree, - 215 \degree,505 \degree,865\degree`

Step-by-step explanation

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

To find angles that are coterminal with
`145 \degree`, we keep adding or subtracting multiples of
`360\degree`

Let us add first to get,


`145 \degree + 360 \degree = 505 \degree`

We add again to get,


`145 \degree + 2(360) \degree = 865\degree`

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


`145 \degree - 360 \degree = - 215 \degree`

We subtract the next multiple to get,


`145 \degree - 2( 360 \degree )= - 575\degree`

This is also the least among the options.

Therefore the angles that are coterminal with 145° are,


`- 575 \degree, - 215 \degree,505 \degree,865\degree`