![]() Firstly, the main difference in the definition is that complementary angles form an angle that measures 90 degrees, and the sum of supplementary angles is 180 degrees. Let’s make a comparison of these two types of angles. Supplementary angles in a parallelogram Complementary vs. supplementary angles ![]() Thus \angle 4 \angle 6=180 \degree, therefore they are supplementary. The proof for this theorem lies in the very definition of supplementary angles, and since \angle 3 and \angle 4 form a linear pair, they are supplementary and by the Alternate Interior Angle Theorem, \angle 3=\angle6. Since, \angle \alpha \angle \gamma=180 \degree, and \angle \gamma \angle \beta=180 \degree, therefore, \angle \alpha and \angle \beta are congruent. Now, we will provide proof for the theorems stated above: Another example of supplementary angles is the opposite of a cyclic quadrilateral. Also, knowing that a parallelogram has opposite angles of equal measure, it is easy to notice that its adjacent ones are supplementary. Therefore, the sum of any two of its angles is supplementary to the third angle. Interestingly, the sum of the angles in a triangle is 180 degrees. The trigonometric connection between supplementary angles: sin (180° – θ) = sin θ Learn more about it in this Cofunction Calculator post. In trigonometry, supplementary angles sines are equal, but their cosines and tangents, unless undefined, are equal in magnitude while having opposite signs. Consecutive angles in a parallelogram are supplementary – One property of parallelograms is that their consecutive angles are supplementary.Same Side Interior Angles Theorem – Interior angles made by a transversal intersecting two parallel lines on the same transversal side are supplementary.Congruent Supplements Theorem – If two angles ( \angle \alpha and \angle \beta ) are both supplementary to a third angle ( \angle \gamma), then \angle \alpha and \angle \beta are congruent.Three geometry theorems mention supplementary angles: In conclusion, the only request for them to be supplementary is to add up to 180 degrees. Therefore, angles don’t need to have common sides or vertex to be supplementary. Sharing a common side is not always a case. That is, they need to create a straight angle while sharing their common side. Two angles combined must have a sum of 180 degrees or \pi radians in order to be supplementary. Check the Angle Conversion post to learn more about conversion between different units. ![]() According to the meaning of “Supplere,” which is to supply, and “Plere” means to fill, we get “when something is supplied to complete a thing.” Now let’s gather all the puzzle pieces and form a precise definition. The word supplementary has its roots in Latin as a combination of words, “Supplere” and “Plere.” The meaning of these two words will set the foundation for the definition of supplementary angles.
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