What is the Difference Between Supplementary and Complementary Angles?
The concept of supplementary angles is important in mathematics and helps students solve geometry questions in class and real life. Recognizing supplementary angles quickly can make problem-solving in exams much easier.
What Is Supplementary Angles?
A supplementary angle is defined as one of a pair of two angles whose measures add up to exactly 180 degrees. You’ll find this concept applied in areas such as straight lines, polygon angle sums, and angles around parallel lines and transversals.
Key Formula for Supplementary Angles
Here’s the standard formula: \( \text{Angle 1} + \text{Angle 2} = 180^\circ \)
To find a missing supplementary angle: \( \text{Supplement} = 180^\circ - \text{Given Angle} \)
Supplementary Angles in Action: Solved Examples
Let’s see a few step-by-step examples of using the supplementary angles formula.
180° – 65° = 115°
2. If two angles are supplementary and one is 98°, what is the other?
180° – 98° = 82°
3. On a straight line, angle A is 123°. What is the measure of angle B?
180° – 123° = 57°
Types of Supplementary Angles
Supplementary angles can be:
- Adjacent: share a common vertex and arm (form a linear pair on a straight line).
- Non-Adjacent: do not share a side or vertex but their measures add up to 180°.
How Are Supplementary Angles Used?
Supplementary angles are not only useful in Maths but also play an important role in Physics, art, engineering, and daily logical reasoning. For example, when designing bridges or reading clock hands on a straight line. Students preparing for competitive exams like JEE or Olympiads will see their importance in angle and geometry questions.
Supplementary vs. Complementary Angles
| Supplementary Angles | Complementary Angles |
|---|---|
| Sum to 180° | Sum to 90° |
| Can be adjacent or not | Can be adjacent or not |
| Often seen as linear pairs or on straight lines | Often seen in right angles or corners |
Tip: "S" for Supplementary angles means "Straight" (forms a straight line), and "C" for Complementary is for "Corner" (forms a right angle).
Step-by-Step Illustration
- Suppose the supplement of x° is 125°.
x + 125° = 180°
x = 180° – 125° = 55°
- Two angles are supplementary. One is twice the other. Find both.
Let smaller angle = y°, Larger angle = 2y°
y + 2y = 180°
3y = 180°
y = 60°, so angles are 60° and 120°
Speed Trick or Easy Shortcut
To instantly find the supplementary angle of any given angle, simply subtract from 180. Many students use this during quick quizzes for accurate and fast solutions.
Example: The supplement of 49° is 180° – 49° = 131°.
Vedantu’s classes cover more such easy shortcuts for students to become faster and smarter in maths!
Practice: Try These Yourself
- What is the supplement of 137°?
- If two angles are supplementary and one is 3 times the other, find both angles.
- Are two 92° angles supplementary?
- Find two non-adjacent supplementary angles that add up to 180°.
Frequent Errors and Misunderstandings
- Mistaking supplementary for complementary angles (remember: 180° vs 90°).
- Forgetting only two angles can be supplementary, not more.
- Assuming angles must be adjacent (they do not have to touch).
- Thinking two obtuse angles can be supplementary (both must together be 180°).
Relation to Other Concepts
The idea of supplementary angles connects closely with complementary angles, types of angles, linear pair of angles, and angle sum property of triangles. Mastering this helps with polygons, parallel lines, and circles in higher geometry topics.
Classroom Tip
A quick way to remember supplementary angles: “If two angles make a straight angle (line), they are always supplementary!” Vedantu’s teachers use this visual cue regularly so students never forget during tests.
We explored supplementary angles—from definition, formula, examples, common mistakes, and connections to other maths topics. Keep practicing with Vedantu for stronger maths skills and clear concept understanding!
More for you: Types of Angles | Linear Pair Angles | Angle Sum Property
FAQs on Supplementary Angles Explained with Examples
1. What are supplementary angles in Maths?
Supplementary angles are two angles whose measures add up to exactly 180 degrees. They form a straight line when placed adjacent to each other. For example, angles measuring 110° and 70° are supplementary because 110° + 70° = 180°.
2. How do I find the supplementary angle if one angle is given?
To find the supplementary angle, subtract the given angle's measure from 180 degrees. For instance, if one angle is 45°, its supplement is 180° - 45° = 135°.
3. What is the difference between complementary and supplementary angles?
Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees. Complementary angles form a right angle, whereas supplementary angles form a straight line when placed together.
4. Are linear pair angles always supplementary?
Yes, a linear pair of angles are always supplementary. A linear pair consists of two adjacent angles formed when two lines intersect; their non-common sides form a straight line, resulting in a sum of 180°.
5. Can two obtuse angles be supplementary?
No, two obtuse angles cannot be supplementary. An obtuse angle measures more than 90° but less than 180°. The sum of two obtuse angles would always exceed 180°.
6. Can two acute angles be supplementary?
No, two acute angles cannot be supplementary. An acute angle measures less than 90°. The sum of two acute angles will always be less than 180°.
7. What are adjacent supplementary angles?
Adjacent supplementary angles share a common vertex and a common side (arm). They lie next to each other and add up to 180°.
8. What are non-adjacent supplementary angles?
Non-adjacent supplementary angles do not share a common vertex or side. Although they are not next to each other, their measures still add up to 180°.
9. How are supplementary angles used in real-life design and construction?
Supplementary angles are crucial in many aspects of design and construction. For example, they are used to ensure that walls meet at right angles (90°), which are supplementary to 90° angles, or that frameworks are stable. They play a vital role in determining angles in buildings, bridges, and other structures.
10. Can three or more angles be supplementary?
While the sum of three or more angles can be 180°, the term 'supplementary' specifically refers to a pair of angles. Therefore, only two angles can be considered supplementary.
11. What is the supplement of a 90° angle?
The supplement of a 90° angle is another 90° angle, as 90° + 90° = 180°.
12. How are supplementary angles related to straight lines?
Supplementary angles always form a straight line when placed adjacent to each other. The sum of their measures equals the measure of a straight angle, which is 180°.
