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Maths · Trigonometrical identities and trigonometrical functions

If one angle of a triangle equals the sum of the other two angles, the triangle

If one angle of a triangle equals the sum of the other two angles, the triangle must be

  • A. scalene
  • B. right angled
  • C. obtuse angled
  • D. acute angled

Step-by-step solution

Let the angles be A, B, C. Given one angle equals sum of other two, say A = B + C. Since A + B + C = 180°, substituting gives (B+C) + B + C = 180° ⇒ 2(B+C)=180° ⇒ B+C=90° ⇒ A=90°. Thus the triangle has a right angle, so it must be right-angled.
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