Find an angle α that is coterminal with an angle measuring −460∘, where 0∘≤α<360∘. Do not include the degree symbol in your answer. For example, if your answer is 20∘, you would enter 20.

Coterminal angles are angles with the same terminal side.

When we have an angle A, the coterminal angles can be written as:

A + k*(360°)

where k can be any integer number. (Notice that when we have k = 0, means that A is coterminal with itself)

Then the set of all the coterminal angles to -225° is:

{-225° + k*360°I k ∈ Z}

where Z is the set of integer numbers.

The coterminal angle is 260°

Step-by-step explanation:

Suppose that we have an angle A.

All the coterminal angles to A are written as:

B = A + n*360°

Where n is any whole number.

Notice that if n = 0, we get:

B = A + 0*360° = A

So A is coterminal with itself, which is trivial.

Now we want to find a conterminal angle to -460° such that it is in the range:

0° < α < 360°

So we just need to find a value of n such that:

α = -460° + n*360°

is on the given range.

We can assume that n = 2 will work, let's check:

α = -460° + 2*360° = 260°

α = 260°

And this angle is in the given range:

0° < 260° < 360°