Can two angle be supplementary if both of them are acute angle
Answers
Answer: Hint: - Condition of supplementary angle is that sum of two angles is equal to 1800
As we know that the condition of supplementary angle is
Sum of two angles is equal to 1800. Let A and B are two angles such that,
⇒∠A+∠B=1800
(i)Acute angle
As we know that acute angle is always less than 900. So, the sum of two acute angle can never make 1800
Therefore the condition of acute angle is
Sum of two angles is less than1800. Let A and B are two angles such that
⇒∠A+∠B<1800
∴Sum of two acute angles cannot make a supplementary angle.
(ii)Obtuse angle
As we know that obtuse angle is always greater than 900. So, the sum of two obtuse angles always makes greater than 1800.
Therefore the condition of obtuse angle is
Sum of two angles is greater than1800. Let A and B are two angles such that
⇒∠A+∠B>1800
∴Sum of two obtuse angles cannot make a supplementary angle.
(iii)Right angle
As we know that the right angle is always equal to 900. So, the sum of two right angles is always equal to 1800.
The condition of right angle is
Sum of two angles is equal to1800. Let A and B are two angles such that
⇒∠A+∠B=1800
∴Sum of two right angles always makes a supplementary angle.
Note: - In such types of questions always remember the condition of supplementary, acute, obtuse and right angles respectively, then we can easily find out which two angles makes a supplementary angle.
$\therefore $Sum of two acute angles cannot make a supplementary angle. As we know that obtuse angle is always greater than ${90^0}$. So, the sum of two obtuse angles always makes greater than ${180^0}$. $\therefore $Sum of two obtuse angles cannot make a supplementary angle.