Fill in the blanks to make the following statements true:

(i) Sum of the angles of a triangle is ....

(ii) An exterior angle of a triangle is equal to the two ....... opposite angles.

(iii) An exterior angle of a triangle is always ......... than either of the interior opposite angles.

(iv) A triangle cannot have more than ...... right angles.

(v) A triangles cannot have more than ......obtuse angles.

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Solution

(i) Sum of the angles of a triangle is 180°.

As we know, that according to the angle sum property, sum of all the angles of a triangle is 180°.

(ii) An exterior angle of a triangle is equal to the two interior opposite angles.

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

As according to the property: An exterior angle of a triangle is equal to the sum of two interior opposite angles. Therefore, it has to be greater than either of them.

(iv) A triangle cannot have more than one right angle.

As the sum of all the angles of a triangle is 180°. So, if the triangle has more than one right angle the sum would exceed 180 °.

(v) A triangle cannot have more than one obtuse angle

As the sum of all the angles of a triangle is 180°. So, if the triangle has more than one obtuse angle the sum would exceed 180 °.

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Similar questions

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.

An exterior angle of a triangle is always greater than either of the interior opposite angles.

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