Question

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

Answer 1

Let ABC be a triangle.
Then,∠A=∠B+∠C
∴∠A+∠B+∠C=180° (Sum of the angles of a triangle)

⇒∠B+∠C+∠B+∠C=180°

⇒2(∠B+∠C)=180°⇒∠B+∠C=90°

⇒∠A=90°( ∵∠A=∠B+∠C)
This implies that the triangle is right-angled at A.