Question

Can two acute angles form a linear pair?

Answer 1

Hint: In this question, we need to tell if two acute angles can form a linear pair or not. For this, we will first understand the definitions of linear pair and acute angles. Using them we will try to find our answer.

Complete step by step answer:
Here we need to tell if acute angles can form a linear pair or not. Let us first understand the meaning of a linear pair. Linear pair is defined as the pair of two angles whose sum is 180 degrees. We can also say supplementary angles form a linear pair. For example, x and y form a linear pair if $ x+y={{180}^{\circ }} $ . Now let us understand the meaning of acute angles. An angle is called an acute angle if its measure is less than 90 degrees. We can say, an angle x is an acute angle if $ x\text{ }<\text{ }{{90}^{\circ }} $ . For example, $ {{80}^{\circ }},{{89}^{\circ }},{{65}^{\circ }},{{40}^{\circ }} $ are all acute angles.

Now let us suppose we have any two acute angles i.e. x and y. We know that they must be less than $ {{90}^{\circ }} $ .
So $ x\text{ }<\text{ }{{90}^{\circ }}\text{ and }y\text{ }<\text{ }{{90}^{\circ }} $ .
Adding them we get, $ x+y\text{ }<\text{ }{{90}^{\circ }}+{{90}^{\circ }} $ .
Adding $ {{90}^{\circ }}+{{90}^{\circ }} $ on the right side we get, $ x+y\text{ }<\text{ }{{180}^{\circ }} $ .
But we want the sum to be equal to $ {{180}^{\circ }} $ to form a linear pair. Therefore, x and y cannot form a linear pair. Hence, we can say that any two acute angles cannot form a linear pair.

Note:
Students should know the definitions of the terms in a sum. Try to create the mathematical form of them and then solve. Students can take an example of acute angles and check that they cannot form a linear pair. For example, even if we take both acute angles as $ {{89}^{\circ }} $ (Less than $ {{90}^{\circ }} $ ) then $ {{89}^{\circ }}+{{89}^{\circ }}={{178}^{\circ }} $ which is less than than $ {{180}^{\circ }} $ and cannot form a linear pair.