prove that triangle must have atleast two acute angle

Explanation

Given `Delta`ABC must have two acute angles
Proof Let us consider the following cases
Case l When two angles are `90^(@) and /_C = 90^(@)`

We know that, the sum of all three angles is `180^(@)`
`:." "/_A + /_B + /_C 180^(@)`
`:." " /_A + /_90^(@) + /_90^(@) = 180^(@)`
`rArr" "/_A + 180^(@) - 180^(@) = 0`
So, no triangle is possible .
Case ll When two angle are abtuse.
Suppose two angles `/_B and /_C ` are more than `90^(@)`.
From Eq. (i),
`/_A + /_B + /_C = 180^(@)`
[`rArr" "/_A + 180^(@) - (90^(@) + /_C)
=90^(@) - /_`C
= Negative angle `" " [: /_`C in abtuse]
Hence, no triangle is possible .
Case IV When two angles are acute, then sum of two angles is less than `180^(@)`, so that the third angle is also acute.