Question

A classmate believes that a triangle can have both a right angle and an obtuse angle. Which of the following statements would you use to convince him that he is incorrect?

Answer 1

Sum of internal angles in a triangle is 180 degree.

∠A + ∠B + ∠C = 180°

Now we have three cases:

Case 1 : For right anlge triangle.

in this case one angle is 90°. and rest of two angle's sum is 90 degree

it means measure of rest two anles is less than 90 degree.

So, this type trianlge holds one right anlge and two acute angle.

Case 2: If one angle is Obtuse angle(more than 90°)

In this case , rest of two angle's sum is less than 90°

So, this type trianlge holds one obtuse anlge and two acute angle.

Case 3: All angles are acute

In this case all three anles are less than 90°

So, triangle has one obtuse angle, that means rest of two anlges must be less than 90°

Answer 2

You can only have obtuse