Question

Explain: Can two acute angles be supplementary?

Answer 1

Hint: We will first understand the terms acute angles and supplementary and then see if the given is possible or not and thus we will get the required answer.

Complete step-by-step solution:
Let us first of all understand the term: Acute angles.
Acute angles: The angles which are less than 90 degrees are known as acute angles.
Now let us understand the term: Supplementary.
Supplementary: The angles which when combined form 180 degrees are known as supplementary angles.
Now, we will assume our two acute angles to be x and y.
So, using the definition we have that x < 90 degrees and y < 90 degrees.
We can write is as two equations:-
$ \Rightarrow x < {90^ \circ }$ ………………..(1)
$ \Rightarrow y < {90^ \circ }$ ………………..(2)
Now, if we add both the equations (1) and (2), we will then obtain:-
$ \Rightarrow x + y < {90^ \circ } + {90^ \circ }$
Simplifying the RHS to get the following expression:-
$ \Rightarrow x + y < {180^ \circ }$
Since, for supplementary angles we require the sum of angles to be ${180^ \circ }$. But here, we are getting the sum of two acute angles to be less than the required. Therefore, the sum of two acute angles cannot be supplementary.

$\therefore $ It is not possible for two acute angles to be supplementary.

Note: The students must notice that they may get some difficulty remembering the difference between acute angles and obtuse angles. Let us make it easier to understand.
You can remember the Acute Angles by the first letter of it that is “A”. Even A has an acute angle inside it, if we look at the angle between two lines, we get an acute angle.
Look at the picture given below to understand the same:

In the word “Supplementary”, we have it starting from ‘S’ that refers to straight and straight refers to straight line and thus 180 degrees.