Question

Which angle is coterminal with a 645° angle?

A. An angle measuring 265°
B. An angle measuring 75°
O C. An angle measuring 285°
D. An angle measuring 345º

Answer 1

C

Explanation:

Coterminal angles are angles that have a common terminal side.

So, given an angle θ, its coterminal angles will always be ±360°. This can be repeated.

We have a 645° angle.

Therefore, all values of the equation:

`645\pm 360n`

Where n is an integer is coterminal with our original angle.

Letting n = 1 and using the negative case, we acquire:

`\Rightarrow 645-360=285`

Therefore, an angle measuring 285° is coterminal with a 645° angle.

None of the other options can be reached by adding/subtracting 360.

Therefore, our answer is C.