Can a triangle have: Two right angles? (ii) Two obtuse angles? Two acute angles (iv) All angles more than `60^0` ? All angles less than `60^0` ? (vi) All angles equal to `60^0`

Explanation

Solution:
(i) Let a triangle 'ABC' has two angles equal to . We know that sum of the three angles of a triangle is '180@'
Hence, if two angles are equal to , then the third one will be equal to zero which implies that 'A, B,C'is collinear, or we can say 'ABC' is not a triangle.
A triangle can’t have two right angles.
(ii) Let a triangle 'ABC' has two obtuse angles
This implies that sum of only two angles will be equal to more than '180@' which contradicts the theorem sum of all angles in a triangle is always equals '180@'.
Therefore, a triangle can’t have two obtuse angles.
(iii) Let a triangle 'ABC' has two acute angles.
This implies that sum of two angles will be less than . Hence third angle will be the difference of '180@' and sum of both acute angles
Therefore, a triangle can have two acute angles.
(iv) Let a triangle 'ABC' having angles are more than '60@ .
This implies that the sum of three angles will be more than '180@' which contradicts the theorem sum of all angles in a triangle is always equals '180@'.
Therefore, a triangle can’t have all angles more than .
(v) Let a triangle 'ABC' having anglesare less than '60@'.
This implies that the sum of three angles will be less than 180° which contradicts the theorem sum of all angles in a triangle is always equals '180@'.
Therefore, a triangle can’t have all angles less than '60@'.
(vi) Let a triangle ABC having angles all equal to '60@'.
This implies that the sum of three angles will be equal to '180@' which satisfies the theorem sum of all angles in a triangle is always equals '180@'.
Therefore, a triangle can have all angles equal to '60@'.