What are supplementary and complementary angles? And how do I find the complement and supplement of an angle measure?

Question

Vedantu Content Team · Accepted Answer

Hint: To write the solution of this question we should first know the meaning of supplementary and complementary angles. These are two types of angles in which the two angles are in pairs and are having a sum of either  $${90^ \circ }$$  or  $${180^ \circ }$$  . Then we will proceed to find the way to find the complement and supplement of the given measure.Complete answer:Pair of angles and definition:Supplementary angles:If the sum of two angles is   $${180^ \circ }$$ , then they are called supplementary angles.Complementary angles:If the sum of two angles is   $${90^ \circ }$$ , then they are called complementary angles.Example For example, angles with measure  $${30^ \circ }\& {150^ \circ }$$  are supplementary angles; where $${30^ \circ }$$  is the supplement of  $${150^ \circ }$$  and vice versa.For example, angles with measure  $${30^ \circ }\& {60^ \circ }$$  are complementary angles; where $${30^ \circ }$$  is the complement of  $${60^ \circ }$$  and vice versa.How to find supplement/ complement Now in order to find a supplement of any given angle we just need to subtract that measure from   $${180^ \circ }$$.For example, we have to find the supplement of   $${50^ \circ }$$.  So we will subtract the measure of this given angle from   $${180^ \circ }$$.Supplement of  $${50^ \circ }$$  =  $${180^ \circ } - {50^ \circ } = {130^ \circ }$$So  $${130^ \circ }$$  is the supplement of  $${50^ \circ }$$  and vice versaNow in order to find a complement of any given angle we just need to subtract that measure from   $${90^ \circ }$$.For example, we have to find the complement of   $${50^ \circ }$$.  So we will subtract the measure of this given angle from   $${90^ \circ }$$.Complement of  $${50^ \circ }$$  =  $${90^ \circ } - {50^ \circ } = {40^ \circ }$$So  $${40^ \circ }$$  is the complement of  $${50^ \circ }$$  and vice versa.Note: Note that complementary angles are always less than or equal to $${90^ \circ }$$ but not in case of supplementary. For supplementary angles the pair can be of acute, obtuse angles. Also note that complementary and supplementary angles may or may not be adjacent. This type of angle is generally used in proofs or in finding the measure of an angle in pairs.

Pair of angles and definition:	Supplementary angles:If the sum of two angles is \[{180^ \circ }\] , then they are called supplementary angles.	Complementary angles:If the sum of two angles is \[{90^ \circ }\] , then they are called complementary angles.
Example	For example, angles with measure \[{30^ \circ }\& {150^ \circ }\] are supplementary angles; where \[{30^ \circ }\] is the supplement of \[{150^ \circ }\] and vice versa.	For example, angles with measure \[{30^ \circ }\& {60^ \circ }\] are complementary angles; where \[{30^ \circ }\] is the complement of \[{60^ \circ }\] and vice versa.
How to find supplement/ complement	Now in order to find a supplement of any given angle we just need to subtract that measure from \[{180^ \circ }\].For example, we have to find the supplement of \[{50^ \circ }\]. So we will subtract the measure of this given angle from \[{180^ \circ }\].Supplement of \[{50^ \circ }\] = \[{180^ \circ } - {50^ \circ } = {130^ \circ }\]So \[{130^ \circ }\] is the supplement of \[{50^ \circ }\] and vice versa	Now in order to find a complement of any given angle we just need to subtract that measure from \[{90^ \circ }\].For example, we have to find the complement of \[{50^ \circ }\]. So we will subtract the measure of this given angle from \[{90^ \circ }\].Complement of \[{50^ \circ }\] = \[{90^ \circ } - {50^ \circ } = {40^ \circ }\]So \[{40^ \circ }\] is the complement of \[{50^ \circ }\] and vice versa.