Question

Is the following statement true and false :

If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

Options

• Ture

• False

Answer 1

If one angle of a triangle is obtuse, then it cannot be a right angles triangle.

According to the angle sum property of the triangle

In ΔABC

∠A +∠B + ∠C = 180°

Now, if it is a right angled triangle

Then, 

∠A + ∠B + ∠C = 180°

90° + ∠B + ∠C =180°

∠B +∠C = 90°

Also if one of the angle’s is obtuse

∠B +∠C > 90°

This is not possible.

Thus, if one angle of a triangle is obtuse, then it cannot be a right angled triangle.