Question

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

Answer 1

let the thee angles of the triangle be 1,2and3 respectively.
given :angle1=angle 2+angle 3
with angle sum property, we have
angle 1+angle 2+ angle 3=180°
since angle 1 + angle 2= angle 1
so, angle 1+angle1=180°
2(angle1)=180°
angle 1 =90°
when 1 angle of a triangle is 90° then the triangle is a right angle triangle.
Hence Proved