Q. 74.1( 76 Votes )

Can two angles be supplementary if both of them are:

(i) Acute

(ii) Obtuse

(iii) Right?

Answer :

(i) If both the angles are acute then two angles can’t be supplementary because:


Acute angle is always less than 90o and addition of any two angles less than 90o can never be equal to 180o


Hence,


Two acute angles cannot be in a supplementary angle pair


(ii) If both the angles are obtuse then two angles can’t be supplementary because:


Obtuse angle is always greater than 90o and addition of any two angles greater than 90o can never be equal to 180o


Hence,


Two obtuse angles cannot be in a supplementary angle pair


(iii) if both the angles are right angles then the pair of angles must be supplementary because:


Right angle is equal to 90o and addition of two right angles is equal to 180o


i.e., 90o + 90o = 180o


Hence,


Two right angles form a supplement angle of pair


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