Complementary Angles

Problems & Solutions

Complementary Agnles: When the sum of two angles is equal to 90o, they are called complementary angles. In this case, both angles are called complementary to each others. For example 30o and 60o, 40o and 50o, 20o and 70o, etc. are complementary angle since their sum is equal to 90o.

Think Discuss and Write

(NCERT Book – Math Class – VII – Page Number – 95)

Question 1: Can two acute angles complement each other?

Explanation: Acute angles are less than 90o. Complementary angles are those angles whose sum is equal to 90o. Thus, complementary angles are always acute angles. Hence, two acute angles can be complementary.

Question 2:Can two obtuse angles complement each other?

Explanation: Two obtuse angles cannot complement each other. Angles greater than 90o are called obtuse angles. Hence, their sum would always be more than ninety degree. Thus, two obtuse angles cannot complement each other.

Question 3: Can two right angles complement each other?

Explanation: Angle equal to 90o is called right angle. Sum of two right angles is 180° which is double the sum of two complementary angles. Hence, it is not possible for two right angles to complement each other.

Try These:

Question 1: Which pairs of following angles are complementary?

Solution: Sum of angles in fig (i) = 70° + 20° = 90°

Hence, they are complementary.

Sum of angles in fig (ii) = 75° + 25° = 100°> 90°

Hence, they are not complementary.

Sum of angles in fig (iii)= 48° + 52° = 100°> 90°

Hence, they are not complementary.

Sum of angles in fig (iv) = 35° + 55° = 90°

Hence, they are complementary.

Question 2: What is the measure of the complement of each of the following angles?
(i) 45º (ii) 65º (iii) 41º (iv) 54º

Solution: We know that the sum of two complementary angles is equal to 90o.
Hence;

1. Complementary of 45º= 90º- 45º= 45º
2. Complementary of 65º= 90º- 65º= 25º
3. Complementary of 41º= 90º- 41º= 49º
4. Complementary of 54º= 90º- 54º= 36º

Question 3: The difference in the measures of two complementary angles is 12o. Find the measures of the angles.

Solution: Let one angle is ‘m’

Therefore, as per question second angle will be m + 12°

We know that the sum of two complementary angle = 90oHence, m + m + 12o = 90o

Or, 2m + 12° = 90°

Or, 2m = 90° - 12° = 78°

Or, m = 78° ÷ 2 = 39°

Second angle = m + 12° = 39° + 12° = 51°

Quesiton 4: Find if the following angles make a complementary pair.

Solution: 27° + 63° = 90°

So, these angles make a complementary pair.

Question 5: Find the complementary angles for following angles:

(a) 15°

Answer: Let us assume the required complementary angle is x

So, 15° + x = 90°

Or, x = 90° - 15° = 75°

Hence, the required complementary angle = 75°

(b) 35°

Answer: Let us assume the required complementary angle is x

So, 35° + x = 90°

Or, x = 90° - 35° = 55°

Hence, the required complementary angle = 55°

(c) 45°

Answer: Let us assume the required complementary angle is x

So, 45° + x = 90°

Or, x = 90° - 45° = 45°

Hence, the required complementary angle = 45°

(d) 60°

Answer: Let us assume the required complementary angle is x

So, 60° + x = 90°

Or, x = 90° - 60° = 30°

Hence, the required complementary angle = 30°

(e) 70°

Answer: Let us assume the required complementary angle is x

So, 70° + x = 90°

Or, x = 90° - 70° = 20°

Hence, the required complementary angle = 20°