Question

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

Answer 1

Given :-

• One angle = Sum of other two angles

To prove :-

• It is a right angled triangle

Solution :-

Let,

1st angle - ∠A

2nd angle - ∠B

3rd angle - ∠C

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∠A + ∠B = ∠C  -- Given

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We know that,

∠A + ∠B + ∠C = 180°

→ ∠C + ( ∠A + ∠B ) = 180°

→ ∠C + ∠C = 180°

→ 2∠C = 180°

→ ∠C = 180/2

→ ∠C = 90°

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∠C = 90° , Therefore the triangle is right angled.

Answer 2

Answer:

The one angle of triangle is equal to the sum of the other two.

Sum of the angle of a triangle = 180

/ A + / B + / C = 180°

/ C + ( / A + / B ) = 180°

/ C + / C = 180°

2 / C = 180°

/ C = 180 /2

/ C = 90°.

So, the Right - angled is proved .