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.

(i) No, two right angles would up to 180o so the third angle becomes zero. This is not possible. Therefore, the triangle cannot have two right angles.

(ii) No, a triangle can’t have two obtuse angles as obtuse angle means more than 90o. So, the sum of the two sides exceeds more than 180o which is not possible. As the sum of all three angles of a triangle is 180o.


(iii) Yes, a triangle can have two acute angle as acute angle means less than 90o.


(iv) No, having angles more than 60o make that sum more than 180o which is not possible as the sum of all angles of a triangle is 180o.


(v) No, having all angles less than 60o will make that sum less than 180o which is not possible as the sum of all angles of a triangle is 180o.


(vi) Yes, a triangle can have three angles equal to 60o as in this case the sum of all three is equal to 180o which is possible. This type of triangle is known as equilateral triangle.


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