Complementary Angles

Problems & Solutions

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

Think Discuss and Write

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

Question 1: Can two acute angles complement each other?

Answer: Yes

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

Question 2:Can two obtuse angles complement each other?

Answer: No

Explanation: Two obtuse angles cannot complement each other. Angles greater than 90^o 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?

Answer: No

Explanation: Angle equal to 90^o 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 90^o.
Hence;

Complementary of `45º= 90º- 45º= 45º`
Complementary of `65º= 90º- 65º= 25º`
Complementary of `41º= 90º- 41º= 49º`
Complementary of `54º= 90º- 54º= 36º`

Question 3: The difference in the measures of two complementary angles is 12^o. 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 = 90^oHence, m + m + 12^o = 90^o

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°