Can two angles be supplementary if both of them are:

(i) Acute? (ii) Obtuse? (iii) Right?

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Solution

(i) No. Acute angle is always lesser than 90º. It can be observed that two

angles, even of 89º, cannot add up to 180º. Therefore, two acute angles cannot be in a supplementary angle pair.

(ii) No. Obtuse angle is always greater than 90º. It can be observed that two angles, even of 91º, will always add up to more than 180º. Therefore, two obtuse angles cannot be in a supplementary angle pair.

(iii) Yes. Right angles are of 90º and 90º + 90º = 180°

Therefore, two right angles form a supplementary angle pair together.

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Similar questions

Q. Can two angles be supplementary if both of them are acute?

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?

Suppose two adjacent angles are supplementary. Show that if one of them is an obtuse angle, then the other angle must be acute.

Question 7 (iii)
Can two angles be supplementary if both of them are:
Right

Question 7 (ii)
Can two angles be supplementary if both of them are:
Obtuse

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Can two angles be supplementary if both of them are: (i) Acute? (ii) Obtuse? (iii) Right?

Can two angles be supplementary if both of them are:

(i) Acute? (ii) Obtuse? (iii) Right?