If one angle of a triangle is greater than the sum of the other two, show that the triangle is obtuse angled.

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Solution

ANSWER:
Let ABC be a triangle and let ∠C>(∠A+∠B)
Then, we have:
2∠C>(∠A+∠B+∠C) ( Adding ∠C to both sides)

⇒2∠C>180° (∵∠A+∠B+∠C=180°)

⇒∠C>90°
Since one of the angles of the triangle is greater than 90°, the triangle is obtuse-angled.

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(v) All the angles of a triangle can be equal to $60^{\circ}$ .

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(viii) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

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(xi) An exterior angle of a triangle is greater than the opposite interior angles.

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