Question

Can a triangle have: 

(i) Two right angles? 

(ii) Two obtuse angles? 

(iii) Two acute angles? 

(iv) All angles more than 60°? 

(v) All angles less than 60°? 

(vi) All angles equal to 60°?

Justify your answer in each case.

Answer 1

(i) No, 

Two right angles would up to 180^o.,So the third angle becomes zero. This is not possible, so a triangle cannot have two right angles. [Since sum of angles in a triangle is 180^o ] 

(ii) No, 

A triangle can’t have 2 obtuse angles. Obtuse angle means more than 90^o So that the sum of the two sides will exceed 180^o which is not possible. As the sum of all three angles of a triangle is 180^o . 

(iii) Yes 

A triangle can have 2 acute angle. Acute angle means less the 90^o angle 

(iv) No, 

Having angles-more than 60^o make that sum more than 18^o Which is not possible [ The sum of all the internal angles of a triangle is 180^o ]

(v) No, 

Having all angles less than 60^o will make that sum less than 180^o which is not possible. [The sum of all the internal angles of a triangle is 180^o] 

(vi) Yes 

A triangle can have three angles are equal to 60^o . Then the sum of three angles equal to the 180^o Which is possible such triangles are called as equilateral triangle. [ The sum of all the internal angles of a triangle is 180^o ]