Question

prove that of one angle of a triangle is equal to the sum of the other two angles, the triangle is right angled​

Answer 1

Answer:

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.

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Answer 2

Answer:

Let, x be one of the angle of the triangle.

Then, the sum of other two angles will be x.

By, angle sum property of a triangle,

x + x = 180°

=> 2x = 180°

=> x = 90°

Therefore, the triangle will be right angled.

Hence, proved.