Question

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

Answer 1

ANSWER
$- 575 \degree, - 215 \degree,505 \degree,865\degree$

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,

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

Answer 2

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,

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