Question

State true or false:

If each angle of a triangle is less than the sum of the other two angles of it then the triangle is acute-angled.

• A. True
• B. False

Answer 1

The correct option is A True

Let the triangle be ABC,
Sum of angles of the triangle,
$\angle A+\angle B+\angle C=180$
$\angle A<\angle B+\angle C$
$\angle A<180-\angle A$
$\angle A<90$
Similarly, $\angle B<90$ and $\angle C<90$
Thus, ABC is an acute angled triangle.