Any two angles are called Supplementary angles when they add up to 180°. When two angles add to 180°, we say that the angles are “Supplement” to each other. In the pair of supplementary angles if one angle is x°, then its supplement is an angle of (180 - x)° .
From the above figures, we have $\angle$ABD and $\angle$DBC are supplementary because 55°+125°=180°. $\angle$EFG and $\angle$HIK are supplementary because 74°+106°=180°. Also, $\angle$ABD and $\angle$DBC together form straight angle $\angle$ABC. Thus, if two angles are together and are supplement to each other then they have a common vertex and share one side. The other two non-shared sides of the angles form a straight line and have a straight angle. Such kind of angles are called as linear pair. The angles need not be together, but together they add up to 180°. For example, in geometrical figures, the adjacent angles of a rectangle are supplementary, and also the opposite angles of a cyclic quadrilateral are supplementary.
Two angles are supplementary, only when one will be an acute angle and the other will be an obtuse angle or both of them will be right angles.
|Congruent Supplementary Angles||What are Angles||Angle of Depression and Angle of Elevation||A Acute Angle|
|A Obtuse Angle||A Right Angle||A Straight Angle||Adjacent Angle|
|All Types of Angles||Angle in Pentagon||Angle Relationship||Angles Complementary|