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Since, the sum of two supplementary angles is 180°.

Therefore, 3x + 7x = 180°
10x = 180°
180°
x = = 18°
10
Thus, the first angle, 3x° = 3 × 18° = 54° and the second angle, 7x = 7 × 18° = 126°.

Example 5: One of two supplementary angles is 32° more than the measure of the smaller. Find
their measures.

Solution: Let one of the supplementary angles be x. Think and Answer
Then, the other angle = x + 32° Can you identify the name of related
Since, the sum of two supplementary angles is 180°. angle formed between the angles

Therefore, x + x + 32° = 180° south-east to south-west and south-
2x + 32° = 180° west to north-west? Name it.
North
2x = 180° – 32° North-West North-East
2x = 148° West East
148°
x = = 74° South-West South-East
2 South

Thus, the first angle = 74°, and second angle = x + 32° = 74° + 32° = 106°
Example 6: Find the angle which is one-third of its supplement.
Solution: Let the angle be x. Then, its supplement = 180° − x.
1
Given, x = (180° – x)
3
⇒ 3x = 180° − x
⇒ 4x = 180°

180°
⇒ x =
4
⇒ x = 45°
Thus, the required angle is 45°.
Example 7: Find the angle whose complement is equal to two-fifths of its supplement.
Solution: Let the angle be x.
Then its complementary angle = 90° − x and supplementary angle = 180° − x
2
Therefore, 90° – x = (180° – x)
5
450° – 5x = 360° – 2x
5x – 2x = 450° – 360°
3x = 90°
90°
x =
3
x = 30°
Thus, the required angle is 30°.

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