Question

prove that a triangle should have at least 2 acute angles

Answer 1

Solution:-
Sum of the three angles of a triangle = 180°
Let us assume that only one angle have to be acute i.e. less than 90°
Then the other two angles will have to be right or obtuse angles (90° or more than 90°)
Let us assume that both the angles are right angles (which is not possible)
Let the third angle be 'x', which is an acute angle.
⇒ 180° = x + 90° + 90°
⇒ x = 180° - 180°
x = 0
We know that an angle of a triangle cannot be 0.
Hence our assumption is completely wrong that two angles of a triangle are right angles. It cannot be possible.
Now, we can say that a triangle must have at least two acute angles.
Hence proved.
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Answer 2

If a triangle has an obtuse or right angle other two angles will be acute as the sum of all the angles of a triangle is 180. So if one angle is 90 or grater than 90 then we are left with the sum of the other two angles as 90 or less than 90 which implies both the angles will be acute only as the sum of angles is 90 or less than 90