Can two angles be supplementary if both of them are:
$(i)$. acute? $(ii)$. obtuse? $(iii)$. right?

To do:

We have to find whether two angles be supplementary if both of them are:

(i) Acute

(ii) Obtuse

(iii) Right

Solution:

(i) We know that,

Acute angle $< 90^{\circ}$

Therefore,

Acute angle $+$ Acute angle $< 90^{\circ}+90^{\circ}$

This implies,

Acute angle $+$ Acute angle $< 180^{\circ}$

Therefore, two acute angles cannot be supplementary angles.

(ii) We know that,

Obtuse angle $> 90^{\circ}$

This implies,

Obtuse angle $+$ Obtuse angle $> 90^{\circ}+90^{\circ}$

Obtuse angle $+$ Obtuse angle $>180^{\circ}$

Therefore, two obtuse angles cannot be supplementary angles.

(iii) We know that,

Right angle $=90^{\circ}$

This implies,

Right angle $+$ Right angle $=90^{\circ}+90^{\circ}$

$=180^{\circ}$

Therefore, two right angles form a supplementary pair.