Can two angles be supplementary if both of them are:

(i) Acute

(ii) Obtuse

(iii) Right?

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

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

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 90^{o} and addition of any two angles greater than 90^{o} can never be equal to 180^{o}

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 90^{o} and addition of two right angles is equal to 180^{o}

i.e., 90^{o} + 90^{o} = 180^{o}

Hence,

Two right angles form a supplement angle of pair

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