# DETERMINE IF ANGLES ARE COTERMINAL

Procedure :

Find the difference between two angles, if it 360 or multiple of 360, they are coterminal. Otherwise they are not.

State if the two given angles are coterminal or not.

Problem 1 :

110º, -250º

Solution :

Step 1 :

Find the difference between the given two angle measures.

110º - (-250º) = 110º + 250º

110º - (-250º) = 360º

Step 2 :

The result of step 1 is

= 360º

= 1(360º)

Which is a multiple of 360º.

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

Problem 2 :

125º, -415º

Solution :

Step 1 :

Find the difference between the given two angle measures.

125º - (-415º) = 125º + 415º

125º - (-415º) = 540º

Step 2 :

The result of step 1 is

= 540º

Which is not a multiple of 360º.

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

Problem 3 :

140º, -220º

Solution :

Step 1 :

Find the difference between the given two angle measures.

140º - (-220º) = 140º + 220º

140º - (-220º) = 360º

Step 2 :

The result of step 1 is

= 360º

= 1(360º)

Which is a multiple of 360º.

So, 140º and -220º 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.

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