Question

The sum of two angles of a triangle is equal to its third angle. Prove that triangle is right angled. ​

Answer 1

☸ Required Answer is ⬇⬇ ⬇⬇ ⬇

c=a + b  

a + b + c = 180  

Substitute c for a +b  

c + c = 180  

2c = 180  

c = 90  

therefore the triangle is a right angled triangle.  

Answer 2

Solution :-

Let the smaller angles be A and CO and greater angle be B.

According to the question,

<B = <A + <C ...... (i)

But, <A + <B + <C = 180° (Sum of all angles of triangle is 180°)

(<A + <C) + <B = 180°

<B + <B = 180° [ Using (i)]

2B = 180°

<B = $\frac {180°}{2}$

<B = 90°

Hence, triangle ABC is right angled.