Question

Every triangle has at least ______ acute angle (s).

Answer 1

We know that, the sum of angles of a triangle is always ${180}^o$.

Let us consider these three possibilities for one of the angles :

(i) Greater than 90° : the sum of remaining two angles must be less than ${90}^o$

Hence, the other two are acute angle.

(i) Exactly 90° : the sum of remaining two angles must be equal to ${90}^o$

Hence, the other two are acute angle.

(ii) Less than 90° : the sum of remaining two angles must be less than ${180}^o$. So, at most one of them may be a right angle or obtuse angle, the other ia an acute angle. Or, both the remaining angles are acute angles.

$\therefore$ In any triangle, two of the interior angles are always acute (less than 90 degrees).