Question

Which of the following statements are true (T) and which are fales (F):

(i) Sum of the three angles of a triangle is ${180}^{\circ }$ .

(ii) A triangle can have two right angles .

(iii) All the angles of a triangle can be less than ${60}^{\circ }$ .

(iv) All the angles of a triangle can be greater than ${60}^{\circ }$.

(v) All the angles of a triangle can be equal to ${60}^{\circ }$.

(vi) A triangle can have two obtuse angles .

(vii) A triangle can have at most one obtuse angle.

(viii) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

(ix) An exterior angle of a triangle is less than either of its interior opposite angles.

(x) An exerior angle of triangle is equal to the sum of the two interior opposite angles.

(xi) An exterior angle of a triangle is greater than the opposite interior angles.

Answer 1

(i) True.

(ii) False. A right triangle has only one right angle.

(iii) False. In this the sum of three angles will be less than ${180}^{\circ }$ which is not true.

(iv) False. In this, the sum of three angles will be more than ${180}^{\circ }$ which is not true.

(v) True . As sum of three angles will be ${180}^{\circ }$ which is true.

(vi) False. A triangle can have only one obtuse angle.

(vii) True.

(viii) True.

(ix) False. Exterior angle of a triangle is always grater than its each interior opposite angles.

(x) True.

(xi) True.