When the sum of the measures of two angles is 180°, such angles are called supplementary angles and each of them is called a supplement of the other.
The vertices of two angles may be same or different. In the given figure ∠AOC and ∠BOC are supplementary angles as ∠AOC + ∠BOC = 180°.
Again, ∠QPR and ∠EDF are supplementary angles as ∠QPR + ∠EDF = 130° + 50° = 180°.
Angles of 60° and 120° are supplementary angles.
The supplement of an angle of 110° is the angle of 70° and the supplement of an angle of 70° is the angle of 110°
Observations:
(i) Two acute angles cannot be supplement of each other.
(ii) Two right angles are always supplementary.
(iii) Two obtuse angles cannot be supplement of each other.
Worked-out Problems on Supplementary Angles:
1. Verify if 115°, 65° are a pair of supplementary angles.
Solution:
115° + 65° = 180°
Hence, they are a pair of supplementary angles.
2. Find the supplement of the angle (20 + y)°.
Solution:
Supplement of the angle (20 + y)° = 180° - (20 + y)°
= 180° - 20° - y°
= (160 - y) °
3. If angles of measures (x — 2)° and (2x + 5)° are a pair of supplementary angles. Find the measures.
Solution:
Since (x - 2)° and (2x + 5)° represent a pair of supplementary angles, then their sum must be equal to 180°.
Therefore, (x - 2) + (2x + 5) = 180
x - 2 + 2x + 5 = 180
x + 2x - 2 + 5 = 180
3x + 3 = 180
3x + 3 – 3 = 180 — 3
3x = 180 — 3
3x = 177
x = 177/3
x = 59°
Therefore, we know the value of x = 59°, put the value in place of x
x - 2
= 59 - 2
= 57°
And again, 2x + 5
= 2 × 59 + 5
= 118 + 5
= 123°
Therefore, the two supplementary angles are 57° and 123°.
4. Two supplementary angles are in the ratio 7 : 8. Find the measure of the angles.
Solution:
Let the common ratio be x.
If one angle is 7x, then the other angle is 8x.
Therefore, 7x + 8x = 180
15x = 180
x = 180/15
x = 12
Put the value of x = 12
One angle is 7x
= 7 × 12
= 84°
And the other angle is 8x
= 8 × 12
= 96°
Therefore, the two supplementary angles are 84° and 96°.
5. In the given figure find the measure of the unknown angle.
Solution:
x + 55° + 40° = 180°
The sum of angles at a point on a line on one side of it is 180°
Therefore, x + 95° = 180°
x + 95° - 95° = 180° - 95°
x = 85°
● Lines and Angles
Fundamental Geometrical Concepts
Some Geometric Terms and Results
Complementary and Supplementary Angles
Parallel and Transversal Lines
8th Grade Math Practice
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