Can two angles be supplementary if both of them are?
$\left( i \right)$Acute, $\left( {ii} \right)$Obtuse, $\left( {iii} \right)$Right?
Answer
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Hint: - Condition of supplementary angle is that sum of two angles is equal to ${180^0}$
As we know that the condition of supplementary angle is
Sum of two angles is equal to ${180^0}$. Let A and B are two angles such that,
$ \Rightarrow \angle A + \angle B = {180^0}$
$\left( i \right)$Acute angle
As we know that acute angle is always less than ${90^0}$. So, the sum of two acute angle can never make ${180^0}$
Therefore the condition of acute angle is
Sum of two angles is less than${180^0}$. Let A and B are two angles such that
$ \Rightarrow \angle A + \angle B < {180^0}$
$\therefore $Sum of two acute angles cannot make a supplementary angle.
$\left( {ii} \right)$Obtuse 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 the condition of obtuse angle is
Sum of two angles is greater than${180^0}$. Let A and B are two angles such that
$ \Rightarrow \angle A + \angle B > {180^0}$
$\therefore $Sum of two obtuse angles cannot make a supplementary angle.
$\left( {iii} \right)$Right angle
As we know that the right angle is always equal to ${90^0}$. So, the sum of two right angles is always equal to ${180^0}$.
The condition of right angle is
Sum of two angles is equal to${180^0}$. Let A and B are two angles such that
$ \Rightarrow \angle A + \angle B = {180^0}$
$\therefore $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.
As we know that the condition of supplementary angle is
Sum of two angles is equal to ${180^0}$. Let A and B are two angles such that,
$ \Rightarrow \angle A + \angle B = {180^0}$
$\left( i \right)$Acute angle
As we know that acute angle is always less than ${90^0}$. So, the sum of two acute angle can never make ${180^0}$
Therefore the condition of acute angle is
Sum of two angles is less than${180^0}$. Let A and B are two angles such that
$ \Rightarrow \angle A + \angle B < {180^0}$
$\therefore $Sum of two acute angles cannot make a supplementary angle.
$\left( {ii} \right)$Obtuse 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 the condition of obtuse angle is
Sum of two angles is greater than${180^0}$. Let A and B are two angles such that
$ \Rightarrow \angle A + \angle B > {180^0}$
$\therefore $Sum of two obtuse angles cannot make a supplementary angle.
$\left( {iii} \right)$Right angle
As we know that the right angle is always equal to ${90^0}$. So, the sum of two right angles is always equal to ${180^0}$.
The condition of right angle is
Sum of two angles is equal to${180^0}$. Let A and B are two angles such that
$ \Rightarrow \angle A + \angle B = {180^0}$
$\therefore $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.
Last updated date: 20th Sep 2023
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