Question

prove that there can be only one right angle or only one obtuse angle in a triangle​

Answer 1

Answer:

From properties of triangle:

Sum of all angles of a triangle is 180 degrees

Right angle means 90 degrees

Obtuse angle means angle greater than 90 degrees

Acute angle means angle less than 90 degrees

Say there is a triangle ABC

A + B + C = 180

From the given data there is one right and one obtuse and one acute.

Let's assume obtuse angle to be 91 degrees. Then

90 + 91 + c = 180

c = -1 (angle of a triangle cannot be negative)

The above simply proves there can be no such triangle. That is “there cannot be a triangle with an obtuse and a right angle in it”.

Hope this answers. Happy learning :)

Answer 2

Answer:

Therefore, a triangle can never have more than one obtuse angle. When an angle of a triangle is 90 degrees, the triangle cannot have an obtuse angle. The other two must each be less than 90 degrees (90 deg + 89 deg + 1 deg = 180 deg).