Question

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

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Answer 1

Given :

• One angle of triangle is equal to the sum of the other two angles.

To Show :

• The triangle is a right angled triangle =?

Step-by-step explanation :

Let, the angles be, ∠A, ∠B and ∠C.

Since we know that the sum of all angles in traingle is 180°, Mathematically, It can be given by,

∠A + ∠B + ∠C = 180°

According to the question, it is given that one angle of triangle is equal to the sum of the other two angles.

Therefore, Let's suppose ∠A + ∠B = ∠C.

It can be written as,

∠A + ∠B + ∠C = 180°

(∠A + ∠B) + ∠C = 180°

∠C + ∠C = 180° [°•° ∠A + ∠B = ∠C]

2∠C = 180°

∠C = 180°/2

∠C = 90°

We know that, 90° angle always makes right angle.

Hence, It is proved!

Answer 2

Answer:

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