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Example 2: If two complementary angles are in the ratio 2 : 3, find the angles.

Solution: Let the first angle be 2x.
Then, the second angle will be 3x.
Since, the sum of two complementary angles is 90°.

Therefore, 2x + 3x = 90°
5x = 90° Think and Answer

90° 1. Can two acute angles be complement of
x = = 18°
5 each other?
Thus, the first angle, 2x = 2 × 18° = 36° 2. Can two obtuse angles be complement of
each other?
and the second angle, 3x = 3 × 18° = 54° 3. Can two right angles be complement of
Supplementary Angles each other?

Two angles are said to be supplementary angles if the sum of their measures is 180°. Each angle
is called the supplement of the other.

Following are some examples of supplementary angles.

N
R
(i) 118° (ii)
62° 112°
68°
L M Q P
In fig (i), sum of the two angles = 118° + 62° = 180°
In fig (ii), sum of the two angles = 68° + 112° = 180°

Knowledge Desk
• Complementary comes from Latin ‘Completum’ meaning "completed", because a right angle is thought
of as being a complete angle.
• 'C' of Complementary stands for "Corner" (a Right Angle), and "S" of Supplementary stands for
"Straight" (180° is a straight angle)

Example 3: Find the supplement of the following angles.
(a) 138° (b) 147° (c) 73° (d) 98°

Solution: Two angles are said to be supplementary if their sum is 180°.
(a) Supplement of 138° = 180° – 138° = 42°

(b) Supplement of 147° = 180° – 147° = 33°
(c) Supplement of 73° = 180° – 73° = 107°

(d) Supplement of 98° = 180° – 98° = 82°
Example 4: If two supplementary angles are in the ratio 3 : 7, find the angles.
Solution: Let the first angle be 3x.

Then, the second angle will be 7x.

151 Lines and Angles