Question

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

Answer 1

One angle of a triangle is equal to the sum of the other two angles 

To Prove: One of the angles is 90° 

Let x, y and z are three angles of a triangle, where 

z = x + y …(1)

Sum of all angles of a triangle = 180° 

x + y + z = 180° 

z + z = 180° (Using equation (1)) 

2z = 180° 

z = 90°

Therefore, triangle is a right angled triangle.