In triangle ABC, angles A and B are acute, and angle C is obtuse. What degree should the sum of angles A

In triangle ABC, angles A and B are acute, and angle C is obtuse. What degree should the sum of angles A and B not exceed so that angle C is obtuse?

We will use the fact that the sum of the angles of any triangle is 180 ° and express the value of the angle C through the values of the angles A and B:
A + B + C = 180;
A + B + C – A = 180 – A;
B + C = 180 – A;
B + C – B = 180 – A – B;
C = 180 – A – B.
Consequently, the value of the angle C will be greater than 90 ° and this angle will be obtuse, provided that the inequality is fulfilled:
180 – A – B> 90.
Transforming this inequality, we obtain:
90 – A – B + A + B – 90> 90 – 90 + A + B;
90> A + B.
Thus, the sum of angles A and B must be less than 90 °.
Answer: the sum of the angles A and B must be less than 90 °.