FINDING UNKNOWN ANGLES IN A SUPPLEMENTARY PAIR

If the measure of two angles adds up to 180 degrees then the angles are called Supplementary Angles.

∠AOC + ∠COB = 180˚

Find the value of x in each supplementary angle pair.

Problem 1 :

Solution :

The sum of the measures of supplementary angles = 180˚.

Here, ∠AOC = x and ∠COB = 100˚

∠AOC + ∠COB = 180˚

x + 100˚ = 180˚

x = 180˚ – 100˚

x = 80˚

So, the value of x is 80˚.

Problem 2 :

Solution :

The sum of the measures of supplementary angles = 180˚.

Here, ∠AOC = 76˚ and ∠COB = x

∠AOC + ∠COB = 180˚

 76˚ + x = 180˚

x = 180˚ - 76˚

x = 104˚

So, the value of x is 104˚.

Problem 3 :

Solution :

The sum of the measures of supplementary angles = 180˚.

Here, ∠AOC = 34˚ and ∠COB = x

∠AOC + ∠COB = 180˚

 34˚ + x = 180˚

x = 180˚ - 34˚

x = 146˚

So, the value of x is 146˚.

Problem 4 :

Solution :

The sum of the measures of supplementary angles = 180˚.

Here, ∠AOC = x and ∠COB = 125˚

∠AOC + ∠COB = 180˚

x + 125˚ = 180˚

x = 180˚ - 125˚

x = 55˚

So, the value of x is 55˚.

Problem 5 :

Solution :

The sum of the measures of supplementary angles = 180˚.

Here, ∠AOC = x and ∠COB = 163˚

∠AOC + ∠COB = 180˚

x + 163˚ = 180˚

x = 180˚ - 163˚

x = 17˚

So, the value of x is 17˚.

Problem 6 :

Solution :

The sum of the measures of supplementary angles = 180˚.

Here, ∠AOC = x and ∠COB = 180˚

∠AOC + ∠COB = 180˚

x + 80˚ = 180˚

x = 180˚ - 80˚

x = 100˚

So, the value of x is 100˚.

Problem 7 :

Solution :

The sum of the measures of supplementary angles =180˚.

Here, ∠AOC = 48˚ and ∠COB = x

∠AOC + ∠COB = 180˚

 48˚ + x = 180˚

x = 180˚ - 48˚

x = 132˚

So, the value of x is 132˚.

Problem 8 :

Solution :

The sum of the measures of supplementary angles = 180˚.

Here, <AOC = 107˚ and <COB = x

<AOC + <COB = 180˚

 107˚ + x = 180˚

x = 180˚ - 107˚

x = 73˚

So, the value of x is 73˚.