Question

Can a triangle have
(i) two right angles?
(ii) two obtuse angles?
(iii) two acute angles?
(iv) each angle more than 60°?
(v) each angle less than 60°?
(vi) each angle equal to 60°?

Answer 1

(i) No
If the two angles are 90^o each, then the sum of two angles of a triangle will be 180^o​, which is not possible.
(ii) No
For example, let the two angles be 120^o and 150^o. Then, their sum will be 270^o​, which cannot form a triangle.
(iii) Yes
For example, let the two angles be 50^o and 60^o​, which on adding, gives 110^o. They can easily form a triangle whose third angle is 180^o $-$ 110^o = 70^o​.
(iv) No
For example, let the two angles be 70^o​ and 80^o, which on adding, gives 150^o. They cannot form a triangle whose third angle is 180^o​ $-$ 150^o = 30^o, which is less than 60^o.
(v) No
For example, let the two angles be 50^o and 40^o, which on adding, gives 90^o . Thus, they cannot form a triangle whose third angle is 180^o $-$ 90^o = 90^o​, which is greater than 60^o.
(vi) Yes
Sum of all angles = 60^o + 60^o + 60^o​ = 180^o