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Exterior Angle Property

Which of the ...

Question

Which of the following statements are true $(T)$ and which are false $(F)$

$i x)$ An exterior angle of a triangle is less than either of its interior opposite angles.

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Solution

Statement: An exterior angle of a triangle is less than either of its interior opposite angles.

The exterior angle of a triangle is equal to sum of the two interior opposite angles.

So, the sum of two Interior angles will always be greater than either of the two interior angles

Hence the statement is False.

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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.

Fill up the blanks to make the following statements true:

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

(b) An exterior angle of a triangle is equal to the sum of ___________ opposite angles.

(d) A triangle cannot have more than ___________ right angle.

(e) A triangle cannot have more than ___________ obtuse angle.

(T)

(F)

x)

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

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