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

Question

Philoid · Accepted Answer

Proof

Let PQR be a right angle triangle,

Now,

∠P = ∠Q + ∠R __________________ (i)

We know that sum of angles of triangle = 180°

∠P + ∠Q + ∠R = 180° [Sum of angles]

⇒ ∠P + ∠P = 180° [From equation (i)]

⇒ 2 ∠P = 180°

⇒ ∠P = 90°

Hence, PQR is a right angle triangle Proved.