DETERMINE IF ANGLES ARE COTERMINAL

State if the two given angles are coterminal or not.

Problem 1 :

110^º, -250^º

Solution :

Step 1 :

Find the difference between the given two angle measures.

110^º - (-250^º) = 110^º + 250^º

110^º - (-250^º) = 360^º

Step 2 :

The result of step 1 is 

= 360^º

= 1(360^º)

Which is a multiple of 360^º.

So, 110^º and -250^º are coterminal angles.

Problem 2 :

125^º, -415^º

Solution :

Step 1 :

Find the difference between the given two angle measures.

125^º - (-415^º) = 125^º + 415^º

125^º - (-415^º) = 540^º

Step 2 :

The result of step 1 is 

= 540^º

Which is not a multiple of 360^º.

So, 125^º and -415^º are not coterminal angles.

Problem 3 :

140^º, -220^º

Solution :

Step 1 :

Find the difference between the given two angle measures.

140^º - (-220^º) = 140^º + 220^º

140^º - (-220^º) = 360^º

Step 2 :

The result of step 1 is 

= 360^º

= 1(360^º)

Which is a multiple of 360^º.

So, 140^º and -220^º are coterminal angles.

Problem 4 :

160º, -380º

Solution :

Step 1 :

Find the difference between the given two angle measures.

160º - (-380º) = 160º + 380º

160º - (-380º) = 540º

Step 2 :

The result of step 1 is 

= 540º

Which is not a multiple of 360º.

So, 160º and -380º are not coterminal angles.

Problem 5 :

Solution :

Step 1 :

Find the difference between the given two angle measures.

Step 2 :

The result of step 1 is

= 4π

= 2(2π)

Which is a multiple of 2π.

So, 19π/18, -53π/18 are coterminal angles.

Problem 6 :

Solution :

Step 1 :

Find the difference between the given two angle measures.

Step 2 :

The result of step 1 is

= -4π

= -2(2π)

Which is a multiple of 2π.

So, 35π/36, 107π/36 are coterminal angles.

Problem 7 :

Solution :

Step 1 :

Find the difference between the given two angle measures.

Step 2 :

The result of step 1 is

= -5π/9

Which is not a multiple of 2π.

So, 41π/36, 61π/36 are not coterminal angles.

Problem 8 :

Solution :

Step 1 :

Find the difference between the given two angle measures.

Step 2 :

The result of step 1 is

= 2π

= 1(2π)

Which is a multiple of 2π.

So, 5π/4, -3π/4 are coterminal angles.

State if the given angles are coterminal.

Problem 9 :

185º, -545º

Solution :

Step 1 :

Find the difference between the given two angle measures.

185º - (-545º) = 185º + 545º

185º - (-545º) = 730º

Step 2 :

The result of step 1 is 

= 730º

Which is not a multiple of 730º.

So, 185º and -545º are not coterminal angles.

Problem 10 :

Solution :

Step 1 :

Find the difference between the given two angle measures.

Step 2 :

The result of step 1 is

= -4π

= -2(2π)

Which is a multiple of 2π.

So, 17π/36, 161π/36 are coterminal angles.