Coterminal angles?

Question

Can someone please give me the answers and explain them because im pretty confused 

Which of the following are not coterminal to 80 degrees? 
A. -46π/9 radians B. -14π/9 radians C. 22π/9 radians D. -32π/9 radians 

Which of the following are not coterminal to 300 degrees? 
A. 1020 degrees B. -420 degrees C. 1140 degrees D. 1320 degrees

Answer 1

(1)

Two angles are said to be co-terminal angles if the sum of two angles are multiples of 360° .

Now check for co-terminals of 80° .

(a)

-46π/9 radians = -920° .

Sum of two angles = │-920│+│80│= 1000 .

1000° is not multiple of 360° . [1000/360 = 2.77 ]

-46π/9 radians is not co-terminal of 80° .

(b)

-14π/9 radians = -280° .

Sum of two angles = │-280│+│80│= 360 .

360° is multiple of 360° .

-14π/9 radians is positive angle co-terminal of 80° .

(c)

22π/9 radians = 440° .

Sum of two angles = │440│-│80│= 360 .

360° is multiple of 360° .

22π/9 radians is negative angle co-terminal of 80° .

(d)

-32π/9 radians = -640° .

Sum of two angles = │-640│+│80│= 720 .

720° is multiple of 360° .

-32π/9 radians is positive angle co-terminal of 80° .

 

Hence -46π/9 radians is not co-terminal of 80° .

Option A is correct.

Answer 2

(2)

Two angles are said to be co-terminal angles if the sum of two angles are multiples of 360° .

Now check for co-terminals of 300° .

(a)

Angle -->1020° .

Sum of two angles for positive angle co-terminal = │1020│+│300│= 1320 .

Sum of two angles for negative angle co-terminal = │1020│-│300│= 720 .

1320° is not multiple of 360° . 

720° is a multiple of 360° .

1020° is negative angle co-terminal of 300° .

(b)

 Angle --> -420° .

Sum of two angles for positive angle co-terminal = │-420│+│300│= 720 .

720° is a multiple of 360° .

-420° is positive angle co-terminal of 300° .

(c)

Angle --> 1140° .

Sum of two angles for positive angle co-terminal = │1140│+│300│= 1440 .

1440 is multiple of 360° .

1140° is positive angle co-terminal of 300° .

 

(d)

Angle -->1320° .

Sum of two angles for positive angle co-terminal = │1320│+│300│= 1620 .

Sum of two angles for negative angle co-terminal = │1320│-│300│= 1020 .

1620 and 1020 are not multiples of 360° .

1320° is not co-terminal of 300° .

 

Hence 1320° is not co-terminal of 300° .

Option D is correct.