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Sum of interior angles of a triangle is 180 degrees.

Side opposite to the greater angle is larger.

Right angled triangle means one angle is equal to 90 degrees.

Construction: -Draw a right angled triangle ABC having $\angle B = {90^ \circ }$, AB is a perpendicular side, BC is a base side and AC is a hypotenuse side.

To prove: - Hypotenuse is a longest side i.e. AC is greater than AB ($AC > AB$) and AC is greater than BC ($AC > BC$)

Proof: -

Now in (As right angled is mentioned in the question)

Also,$\angle ABC + \angle BCA + \angle CAB = {180^ \circ }$ (Sum of interior angles of a triangle is 180 degree)

$ \Rightarrow {90^ \circ } + \angle BCA + \angle CAB = {180^ \circ }$

$ \Rightarrow \angle BCA + \angle CAB = {180^ \circ } - {90^ \circ }$

$\therefore \angle BCA + \angle CAB = {90^ \circ }$

$ \Rightarrow \angle BCA$ and $\angle CAB$ are acute angles so they will be less than 90 degree.

$\therefore \angle BCA < {90^ \circ }$ and $\angle CAB < {90^ \circ }$

Therefore $\angle BCA < \angle ABC$ and $\angle CAB < \angle ABC$

$ \Rightarrow AC > AB$ and $AC > BC$ (Side opposite to greater angle is larger)

Thus hypotenuse AC is the longest side.

$\angle BCA + \angle CAB = {90^ \circ }$

Then possibilities of values of angles will be: -

45 and 45

30 and 60

60 and 30

20 and 70

70 and 20

Therefore in all these cases we find that all the angles are less than 90 degree.