Question

Find the Supplement angle of \[60\% \] of \[{100^\circ }\] .

Answer 1

Hint: We have to find the value of the supplement angle of \[60\% \] of \[{100^\circ }\] . We solve this question using the concept of properties of angles and the concept of percentage . First we will find the percentage of the given angle and then using the concept of the supplements of angles we will subtract the angle from the supplementary angle and we will solve for the value of the supplement of the given condition .

Complete step-by-step solution:
Given : supplement angle of \[60\% \] of \[{100^\circ }\]
Now , let us consider that the \[60\% \] of \[{100^\circ }\] is an angle \[x\] .
Now , we will find the value of \[x\]
We , also know that the percentage of a number is written as :
\[x\% {\text{ }}of{\text{ }}b = \dfrac{x}{{100}} \times b\]
Using this , we get the value of \[x\] as :
\[x = \;60\% \] of \[{100^\circ }\]
Which can be written as :
\[x = \;\dfrac{{60}}{{100}} \times {100^\circ }\]
On solving this expression we get the value of \[x\] as :
\[x = \;{60^\circ }\]
Now , we have to find the supplement angle of \[x\] .
We also know that the supplement of the angle can be calculated as the subtraction of the given angle from the supplementary angle .
We also know that a supplementary angle is equal to \[{180^\circ }\] .
Supplement angle of x can be written as :
\[\text{Supplement angle} = {180^\circ } - x\]
Putting the values , we get
\[\text{Supplement angle} = {180^\circ } - {60^\circ }\]
\[\text{Supplement angle} = {120^\circ }\]
Hence , the supplement angle of \[60\% \] of \[{100^\circ }\] is \[{120^\circ }\] .

Note: Supplementary angle : It is stated as the sum of a pair of angles which is equal to \[{180^\circ }\] . An angle whose measure is equal to \[{180^\circ }\] is known as supplementary angle . It is also known as a straight angle .
Make sure to differentiate between a supplementary angle and a complementary angle as you might exchange the values of the both and result in the wrong solution .