Question

Can two acute angles form a linear pair?

Answer 1

Hint: - Here we go through by the definition of a linear pair that means two adjacent angles that are supplements. And we know that the definition of acute angles. By these definitions we will get to your answer.

Complete step-by-step answer:
As we know that the definition of a linear pair are two adjacent angles that are supplements (form a 180 degree angle together).
And Acute, by definition, is an angle that is smaller than 90 degrees.
Let x represent the measure of an acute angle, and let y represent the measure of another acute angle.
i.e. $x < {90^0}$ let it be equation (1)
And $y < {90^0}$ let it be equation (2).
Now add these equations we get,
$
   \Rightarrow x + y < {90^0} + {90^0} \\
   \Rightarrow x + y < {180^0} \\
 $
Because the sum of the measures of two acute angles is always less than 180 degrees, two acute angles can never form a linear pair.

Note: - Whenever we face such a type of question the key concept for solving the question is first find out the definition of the terms that are given in the question and then let some variables according to the definition and by writing these variables in mathematical terms we will observe our answer.