Can two obtuse angles be supplementary?

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Solution

Two Angles are Supplementary when they add up to $180^{\circ}$ .

Let us consider the least obtuse angle, i.e., $> 90^{\circ}$ Say $91^{\circ}$ and add it to itself.

$91^{\circ} + 91^{\circ} = 182^{\circ}$

This is $> 180^{\circ}$ . Hence, two obtuse angles can never be supplementary.

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Two obtuse angles can be supplementary angles.

Answer the following questions and justify.
(i) Can two acute angles he complement to each other?
(ii) Can two obtuse angles be complement to each other?
(iii) Can two right angles he complement to each other?
(iv) Can two acute angles be supplementary?
(v) Can two obtuse angles be supplementary?
(vi) Can two right angles be supplementary?
(vii) Can two adjacent angles be supplementary?
(viii) Can two adjacent angles be complementary?
(ix) Can two obtuse angles be adjacent angles?
(x) Can an acute angle be adjacent to an obtuse angle?
(xi) Can two acute angles form a linear pair?
(xii) can two obtuse angles form a linear pair?
(xiii) Can two right angles form a linear pair?