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
•
Total views: 213.9k
•
Views today: 4.92k
Answer
213.9k+ views
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.
Recently Updated Pages
Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
