Question

Which measure is of an angle that is coterminal with a 95° angle? 95° " (1,450n)°, for any integer n 95° " (1,080n)°, for any integer n 95° " (780n)°, for any integer n 95° " (340n)°, for any integer n

Answer 1

The answer to your problem is, A. 95° + 360°n, for any integer n.

Explanation:

First you would need to simplify the problem:

1. 95° + 360°n, for any integer n
2. 95° - 360°n, for any integer n

Techniquelly 2nd is the answer.

How you find a coterminal:

Example:

Find the coterminal angle of 11pi/3?

Subtract 2π 2 π from 11π3 11 π 3 .

The resulting angle of 5π3 5 π 3 is positive, less than 2π 2 π , and coterminal with 11π3 11 π 3 .

Thus the answer to your problem is, 95° + 360°n, for any integer n.

Answer 2

An angle is coterminal with another angle if they have the same initial and terminal sides. To find an angle that is coterminal with a 95° angle, we can add or subtract a multiple of 360° (one full rotation) to the original angle.

So the measures that are coterminal with a 95° angle can be expressed as:

95° + 360°n, for any integer n (to get a larger positive angle)

or

95° - 360°n, for any integer n (to get a smaller positive angle)

Simplifying these expressions, we get:

(1) 95° + 360°n, for any integer n

(2) 95° - 360°n, for any integer n

Note that options (1) and (2) represent the same set of angles, since adding or subtracting multiples of 360° does not change the angle's position or orientation.

Option (3) includes angles that are less than one full rotation (less than 360°) and therefore cannot be coterminal with a 95° angle.

Option (4) includes angles that are greater than one full rotation and therefore overlap with option (1).

Therefore, the measure that is coterminal with a 95° angle is option (1): 95° + 360°n, for any integer n.

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