Question

if one angle of a triangle is equal to the sum of the other two,show that the triangle is right angled.​

Answer 1

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

GIVEN:

♦The one angle is equal to the sum of other two angles.

TO PROVE:

♦ The ∆ is right angled triangle.

PROOF:

Let us take the angles be x° , y° and z°.

Now, Let that x is the angle whose measure is equal to the sum of other two angles.

So,

$\large\red{\boxed{ x = y + z}}$

Now in a ∆ we know that sum of the angles is 180°

So,

$\huge\green{\boxed{ x+y+z=180°}}$

=> $x + y + z = 180°$

=>$x + x = 180°$

(just showed that x = y + z)

=> $2x = 180°$

=>$x =\dfrac{180°}{2}$

=>$x = 90°$

Hence one angle of the ∆ is 90° , so it is a right angled ∆.