**Two angles of a triangle are always acute; third angle can be acute, obtuse, or a right.**

**CASE I: All angles are acute**

Since all angles are acute, we don’t need to prove anything in this case as it agrees to our statement.

**CASE II: One angle is GREATER THAN or EQUAL to 90 degrees**

Since sum of all angles of a triangle is 180 degrees; If one angles is greater than or equal to 90 degree, sum of other two angles has to be less than or equal to 90 degree

A + B + C = 180 …. (1)

Since A >= 90 …. (2)

Add B + C on both sides of equation (2)

A + B + C >= 90 + B + C

=> 180 >= 90 + B + C

=> B + C <= 180 – 90

=> B + C <= 90

=> B < 90 & C < 90

So, we see that the other two angles are always acute in this case as well.