Two angles are complementary. one contains 30° more than the other. find both angles. the measures of the angles are degrees.

Solution:

Two angles are said to be complementary if their sum is 90°. The two angles θ₁ and θ₂ are said to be complementary.

Let  θ₁ = θ₂ + 30°(Given)(1)

As per the condition of complementarity we have

θ₁ + θ₂ =  90°

Substituting (1) in the equation above we get

 θ₂ + 30° + θ₂ = 90°

2θ₂ =  90° - 30°

2θ₂ =  60°

θ₂ =  30°

Therefore 

Θ₁ = θ₂ + 30°

Θ₁ = 30° + 30°

Θ₁  = 60°

Thus Θ₁  = 60° and θ₂ =  30°

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Two angles are complementary. one contains 30° more than the other. find both angles. the measures of the angles are degrees.

Summary:

The two angles complementary. Angles are 60° and 30° respectively.