Can a triangle have:
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.

Solution:

(i) No, Two right angles would up to 180°. 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°]

(ii) No, A triangle can’t have 2 obtuse angles. Obtuse angle means more than 90° So that the sum of the two sides will exceed 180° which is not possible. As the sum of all three angles of a triangle is 180°.

(iii) Yes, A triangle can have 2 acute angles. Acute angle means less the 90° angle.

(iv) No, Having angles more than 60° make that sum more than 180°. This is not possible. [Since the sum of all the internal angles of a triangle is 180°]

(v) No, Having all angles less than 60° will make that sum less than 180° which is not possible.[Therefore, the sum of all the internal angles of a triangle is 180°]

(vi) Yes, A triangle can have three angles equal to 60°. Then the sum of three angles equal to the 180°. Such triangles are called as equilateral triangle. [Since, the sum of all the internal angles of a triangle is180°]

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