Question

If a statement is that angle A and B are complementary, which fact would be needed to prove that this geometric relationship is true?
1. The Sum of the angles is 180.
2. The angles are vertical angles.
3. The two angles are equal to each other.
4. The sum of the angles is 90.

Answer 1

The statement that tells ∠A and ∠B are complementary is The sum of angles is 90

What is complementary angles?

Complementary angles are those whose combined angle is 90 degrees or less. To put it another way, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.

Consider the case where one angle is x and the other is 90° - x. Thus, for trigonometric ratios when one ratio is complementary to another ratio by 90 degrees, such as; we employ these complimentary angles.

sin (90° – A) = cos A

cos (90° – A) = sin A

tan (90° – A) = cot A

cot (90° – A) = tan A

sec (90° – A) = cosec A

cosec (90° – A) = sec A

Hence, you can see here the trigonometric ratio of the angles gets changed if they complement each other.

As per the definition of complimentary angles if the sum of the angles is equal to 90 then they are complimentary

∴ The statement 4 is correct .

To learn more about complementary angles from the given link  

brainly.com/question/16281260

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