Question

if one angle of a triangle is equal to the sum of the other two angles then prove that triangle is a right angle triangle​

Answer 1

EXPLAINATION

Let ABC be a triangle such that C is the greatest angle, then

∠A + ∠B = ∠C --------(1)

Also

∠A + ∠B + ∠C = 180º

or ∠C + ∠C = 180º (Using (1))

or 2∠C = 180º

or ∠C = 90º

Hence, triangle ABC is proved to be a right triangle.

Answer 2

Answer:

Sol: Given - B = A+C ------(1)

In ABC ,By Angle Sum Property of Triangle,

A +B+C = 180°

B + (A+C) = 180°

B + B = 180° [From equation (1)]

2B = 180°

B = 180°/2 = 90°

Now ,here B =90° it means ABC is a right angled triangle