FINDING UNKNOWN ANGLES IN A COMPLEMENTARY PAIR

If the measure of two angles adds up to 90 degrees then the angles are called Complementary Angles.

∠AOB + ∠BOC = 90˚

Find the value of x in each right angle.

Problem 1 :

Solution :

The sum of the measures of complementary angles = 90˚.

Here, ∠AOC = x and ∠COB = 45˚

∠AOC + ∠COB = 90˚

x + 45˚ = 90˚

x = 90˚ – 45˚

x = 45˚

So, the value of x is 45˚.

Problem 2 :

Solution :

The sum of the measures of complementary angles = 90˚.

Here, ∠AOC = 72˚ and ∠COB = x

∠AOC + ∠COB = 90˚

 72˚ + x = 90˚

x = 90˚ - 72˚

x = 18˚

So, the value of x is 18˚.

Problem 3 :

Solution :

The sum of the measures of complementary angles = 90˚.

Here, ∠AOC = 23˚ and ∠COB = x

∠AOC + ∠COB = 90˚

23˚ + x = 90˚

x = 90˚ - 23˚

x = 67˚

So, the value of x is 67˚.

Problem 4 :

Solution :

The sum of the measures of complementary angles = 90˚

Here, ∠AOC = 81˚ and ∠COB = x

∠AOC + ∠COB = 90˚

81˚ + x = 90˚

x = 90˚ - 81˚

x = 9˚

So, the value of x is 9˚.

Problem 5 :

Solution :

The sum of the measures of complementary angles = 90˚.

Here, ∠AOC = x and ∠COB = 17˚

∠AOC + ∠COB = 90˚

x + 17˚= 90˚

x = 90˚ - 17˚

x = 73˚

So, the value of x is 73˚.

Problem 6 :

Solution :

The sum of the measures of complementary angles = 90˚.

Here, ∠AOC = 43˚ and ∠COB = x

∠AOC + ∠COB = 90˚

43˚ + x = 90˚

x = 90˚ - 43˚

x = 47˚

So, the value of x is 47˚.

Problem 7 :

Solution :

The sum of the measures of complementary angles = 90˚.

Here, ∠AOC = 77˚and ∠COB = x

∠AOC + ∠COB = 90˚

77˚ + x = 90˚

x = 90˚ - 77˚

x = 13˚

So, the value of x is 13˚.

Problem 8 :

Solution :

The sum of the measures of complementary angles = 90˚.

Here, ∠AOC = x and ∠COB = 68˚

∠AOC + ∠COB = 90˚

x + 68˚ = 90˚

x = 90˚ - 68˚

x = 22˚

So, the value of x is 22˚.