☯GIVEN : a) 53° b) 45° c) 19° d) 69° e) 81° ☯TO FIND : Complement of each angles. ☯KNOWLEDGE REQUIRED : Two angles are said to be complementary , if the sum of two angles is equal to 90°. ➲SOLUTION : Let complement in each case be x°. a) 53° [tex]\implies{ \sf{53 ^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\ [/tex] [tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 53 ^ { \circ}} } \\ \\[/tex] [tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^ { \circ}= 37 ^ { \circ}} }}}}[/tex] [tex]\huge {\pink{\therefore}}[/tex] The complement of 53° is 37°. b) 45° [tex]\implies{ \sf{45^ {\circ} + x^ { \circ} = 90^ { \circ}} } \\ \\ [/tex] [tex] \implies{ \sf{ x^ { \circ} = 90 ^ { \circ}- 45^ { \circ}} } \\ \\[/tex] [tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^ { \circ}= 45 ^ { \circ}} }}}}[/tex] [tex]\huge {\pink{\therefore}}[/tex] The complement of 45° is 45°. c) 19° [tex] \implies{ \sf{19^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\ [/tex] [tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 19^ { \circ}} } \\ \\ [/tex] [tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^{ \circ}= 71 ^ { \circ}} }}}}[/tex] [tex]\huge {\pink{\therefore}}[/tex] The complement of 19° is 71°. d) 69° [tex] \implies{ \sf{69^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\ [/tex] [tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 69^ { \circ}} } \\ \\[/tex] [tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^ { \circ}=21 ^ { \circ}} }}}}[/tex] [tex]\huge {\pink{\therefore}}[/tex] The complement of 69° is 21°. e) 81° [tex] \implies{ \sf{81^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\[/tex] [tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 81^ { \circ}} } \\ \\[/tex] [tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^{\circ}=9 ^ { \circ}} }}}}[/tex] [tex]\huge {\pink{\therefore}}[/tex] The complement of 81° is 9°. Reply
☯GIVEN :
☯TO FIND :
☯KNOWLEDGE REQUIRED :
➲SOLUTION :
Let complement in each case be x°.
[tex]\implies{ \sf{53 ^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\ [/tex]
[tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 53 ^ { \circ}} } \\ \\[/tex]
[tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^ { \circ}= 37 ^ { \circ}} }}}}[/tex]
[tex]\huge {\pink{\therefore}}[/tex] The complement of 53° is 37°.
[tex]\implies{ \sf{45^ {\circ} + x^ { \circ} = 90^ { \circ}} } \\ \\ [/tex]
[tex] \implies{ \sf{ x^ { \circ} = 90 ^ { \circ}- 45^ { \circ}} } \\ \\[/tex]
[tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^ { \circ}= 45 ^ { \circ}} }}}}[/tex]
[tex]\huge {\pink{\therefore}}[/tex] The complement of 45° is 45°.
[tex] \implies{ \sf{19^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\ [/tex]
[tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 19^ { \circ}} } \\ \\ [/tex]
[tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^{ \circ}= 71 ^ { \circ}} }}}}[/tex]
[tex]\huge {\pink{\therefore}}[/tex] The complement of 19° is 71°.
[tex] \implies{ \sf{69^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\ [/tex]
[tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 69^ { \circ}} } \\ \\[/tex]
[tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^ { \circ}=21 ^ { \circ}} }}}}[/tex]
[tex]\huge {\pink{\therefore}}[/tex] The complement of 69° is 21°.
[tex] \implies{ \sf{81^ {\circ} + x^ { \circ}= 90^ { \circ}} } \\ \\[/tex]
[tex]\implies{ \sf{ x^ { \circ}= 90 ^ { \circ}- 81^ { \circ}} } \\ \\[/tex]
[tex]\implies{ \underline{ \boxed{ \red{ \bf{ x^{\circ}=9 ^ { \circ}} }}}}[/tex]
[tex]\huge {\pink{\therefore}}[/tex] The complement of 81° is 9°.
Answer:
a. 37
b. 90
c. 71
d. 21
e. 9
Step-by-step explanation:
hope it helps u