Question

If each angle of triangle is less than the sum of other two,show that the triangle is obtuse angle

Answer 1

Answer:

Let ∠A+∠B+∠C=180°- be angles of triangle

Given:

∠A < ∠B+∠C, ∠B < ∠A+∠C, ∠C < ∠A+∠B

Since ∠B+∠C = 180°- ∠A, we can put the inequality as:

∠A < 180°- ∠A

2∠A  < 180°

∠A  < 90°, so ∠A  is acute angle

Similarly,

we can show that ∠B and ∠C  are acute angles as well

So this triangle has no obtuse angles and it is acute angled triangle