# Can two angles be supplementary if both of them are?

$\left( i \right)$Acute, $\left( {ii} \right)$Obtuse, $\left( {iii} \right)$Right?

Last updated date: 25th Mar 2023

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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.

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