Q11 of 153 Page 144

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

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.


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