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Complementary Angles:

Set of two angles when added, results in 90 degrees, are said to be complementary angles. If two angles are together, that is sharing a common vertex and forming a right angle, then this set of angles will be called adjacent complementary angles. And, if two angles are not adjacent, yet summing up to 90 degrees, then it will be called a non-adjacent complementary angle.


Condition for two angles x,y to be complementary angle:  x+y=90°

 

Complementary Angles Sample Questions:

Question 1: Find the unknown angle in the following figure.
 

 

Triangle Image 1


Answer: 49°

Explanation: The given set of angles are complementary, as they form a right angle.

 

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Question 2: The following angles are complementary. Find the value of the unknown angle.


Triangle Image 2


Answer: 30°

Explanation: The given set of angles are complementary.

 

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Question 3: The following angles are complementary. Find the value of a.


Triangle Image 3

 

Answer: a= 54°

Explanation: The given set of angles are complementary.

 

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Question 4: Find the measure of x.


Triangle Image 5


Answer: x= 22.5°

Explanation: The given set of angles are complementary, as they form a right angle.

 

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Question 5: Given ABC is a right-angled triangle. Identify the complementary angles.


Triangle Image 6


Answer: ∠ABD, ∠CBD

Explanation: Two angles with vertex B, make a right angle. Hence, they are complementary angles,

 

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Question 6: Given BAC is a right-angled triangle. Identify the complementary angles.


Triangle Image 7


Answer: ∠BAD, ∠CAD

Explanation: Two angles with vertex A, make a right angle. Hence, they are complementary angles,

 

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Question 7: Given PQR is a right angle. Find the measure of the other two angles.


Triangle Image 8


Answer: ∠PQS=70°, ∠RQS=20°

Explanation: The given set of angles are complementary, as they form a right angle.

 

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Question 8: Given ABC is a right angle. Find the measure of the other two angles.



Answer: ∠ABD=65°, ∠CBD=25°

Explanation: The given set of angles are complementary, as they form a right angle.

 

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Question 9: Two complementary angles have a proportion of 6:5. Find their measure.


Answer: 49°, 41°

Explanation: Let us assume the angle be 6x°, 5x°. As they are complementary, their sum would be 90°.

 

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Question 10: Two complementary angles have a proportion of 7:3. Find their measure.


Answer: 63°, 27°

Explanation: Let us assume the angle be 7x°, 3x°. As they are complementary, their sum would be 90°.

 

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Frequently Asked Questions:

Question 1: What are complementary angles?

Two angles whose sum is equal to 90° degree are known as complementary angles.

 

Question 2: What do complementary angles add up to?

Complementary angles add up to 90°, 

angleA+angleB=90°.
 

Question 3: How to find complementary angles?

We know that the total of two complementary angles equals 90 degrees, and that each of them is called a "complement."

As a result, finding the complement of an angle is as simple as subtracting it from 90 degrees.

If x° is one of the angles then its complement is 90-x°.

 

Question 4: What is formed when two complementary angles share one ray?

Two complementary angles share one ray to make a right angle.Because two complementary angles add up to 90 degrees, a right angle.

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