Question

Which measure is of an angle that is coterminal with a 425 degree angle

A. 425 degree-(1,000n)degree, for any integer n
B.425 degree-(840n)degree, for any integer n
C. 425 degree+(960n)degree, for any integer n
D. 425 degree+(1,440n)degree, for any integer n

Answer 1

D. 425° + (1,440n)°, for any integer n

Answer 2

We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.

We have been given an angle 425 degrees.

From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.

Let us check each of the options one by one.

(A) The angle being subtracted is
`1000n`. Therefore, we have
`(1000n)/(360)=2.77n`, which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(B)

The angle being subtracted is
`840n`. Therefore, we have
`(840n)/(360)=2.33n`, which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(C)

The angle being added is
`960n`. Therefore, we have
`(960n)/(360)=2.67n`, which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(D)

The angle being added is
`1440n`. Therefore, we have
`(1440n)/(360)=4n`, which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.

Hence, correct answer is option (D).