Question

Which expression finds the measure of an angle that is coterminal with a 126° angle?

126° + (275n)°, for any integer n
126° + (375n)°, for any integer n
126° + (450n)°, for any integer n
126° + (720n)°, for any integer n

Answer 1

All the coterminal angles with 126° are 126 + k*360, being k an integer.

if you make k=2n

You find that 126° + 2n*360 also represent coterminal angles for 126°, so the answer is 126° + 720n

Answer 2

126° + (720n)°, for any integer n

Explanation:

Coterminal Angles of an angle are the angles who share the same initial side and terminal sides.

Also, we can find the coterminal angle of an angle by adding or subtracting 360°. ( When angle is given in degree ),

For example, if Ф is an angle,

Then, its coterminal angles are,

Ф + 360 n, for an integer n,

Here, Ф = 126°,

Hence, its coterminal angles are,

126° + ( 360 n)°,

Since, n is an integer,

⇒ 2n is an integer,

So, the co-terminal angle of 126° can be written,

126° + ( 360×2n )°= 126° + ( 720n)°, for any integer n.