Complementary Angles and Supplementary Angles Theorem
Complementary and Supplementary Angles theorem are added below,
Complementary Angle Theorem
Complementary Angle Theorem states that if the sum of the measures of two angles is 90 degrees, then the angles are complementary. In mathematical terms, if ∠x + ∠y = 90° then ∠x and ∠y are complementary angles.
For example, if you have an angle measuring 30° the complementary angle would be 60° because 30° + 60° = 90°.
Supplementary Angle Theorem
Supplementary angle theorem states that if two angles are supplementary to the same angle, then the two angles are said to be congruent.
Proof:
If ∠x and ∠y are two angles that are supplementary to a third angle ∠z, then,
∠x + ∠z = 180 ……. (1)
∠y + ∠z = 180 ……. (2)
Then, from the above equations, we can conclude,
∠x = ∠y
Hence Proved
Complementary and Supplementary Angles
Complementary and Supplementary Angles are the pairs of angles whose sum is 90° and 180° respectively.
Complementary angles are pairs of angles whose measures add up to 90 degrees. In other words, when you have two complementary angles, the sum of their measures equals a right angle.
Supplementary angles are nothing but when the sum of two angles is equal to the straight line angle or 180 degrees. Supplementary angles are frequently encountered in various geometric shapes, such as parallelograms and straight lines.
In this article, we will learn about, supplementary angles and complementary angles, how to find the complementary and supplementary angles, their differences, and some practice questions on the above. Let’s start by understanding the definition of angle and its types.
Table of Content
- Definition of Angle
- Types of Angles
- What is Complementary Angle?
- Complementary Angle Definition
- How to Find Complementary Angle?
- What is Supplementary Angle?
- Supplementary Angle Definition
- How to Find Supplementary Angle?
- Adjacent Supplementary Angles and Complementary Angles
- Non-Adjacent Complementary and Supplementary Angles
- Complementary Angles and Supplementary Angles Theorem
- Complementary Angle Theorem
- Supplementary Angle Theorem
- Difference Between Supplementary Angles and Complementary Angle
- Real-Life Examples of Complementary Angles and Supplementary Angles
- Complementary and Supplementary Angle Formulas
- Complementary Angles
- Supplementary Angles
- Calculation of Supplementary and Complementary Angles
- Practice Questions on Complementary Angles and Supplementary Angles