Question

How do you find the complement and supplement of an angle if the angle is $85$ degrees?

Answer 1

Hint: If we know what is complement angle and supplement angle then we can easily solve the given problem. Complement angles are those when angles get added then the sum will be $90$ degrees and supplement angles are those whose sum is $180$ degrees. By using these concepts we can easily arrive at the solution.

Complete step by step solution:
In this question they have asked to find the complementary angle and supplementary angle.
Now we need to understand what is complement and supplement angles are:
Complementary angles:
Complementary angles are nothing but the two angles whose sum is equal to $90$ degrees. An example for complementary angles are shown as in the below figure:

From the above diagram we can see that angle $ABC$ and angle $CBD$ makes a sum of angles of $90$ degrees which is complementary angles.
Supplementary angles:
Supplementary angles are nothing but the two angles whose sum is equal to $180$ degrees. An example for supplementary angles are shown as in the below figure:

From the above diagram we can see that angle $ABC$ and angle $CBD$ makes a sum of angles of $180$ degrees which is supplementary angles.
Now they have asked to find a complement of $85$ degrees, so for this let us consider $x$ be the complement angle. Therefore we can write as
$85 + x = 90$
$ \Rightarrow x = 90 - 85$
Therefore, $x = 5$ degrees
The complement angle of $85$ degrees is $5$ degree.
To find supplement angles, we know the sum of angles should be $180$ degrees, so let $x$ be the supplement angle to be calculated, so we can write as
$85 + x = 180$
$ \Rightarrow x = 180 - 85$
Therefore, $x = 95$ degrees

Hence, the supplement angle of $85$ degrees is $95$ degrees.

Note:
If you know the condition for complementary angles and supplementary angles, then directly you can substitute and calculate for the required angle. While calculating just be careful about the sum of angles so that you can arrive at the correct solution.