Question

7. Three angles of a triangle are x°, 2x® and 3x°. Prove that the triangle is right angled.
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Answer 1

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★ Three angles of a triangle are x°, 2x® and 3x°. Prove that the triangle is right angled.

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Given :-

Three angles of a triangle are x°, 2x° and 3x°.

To Prove :-

The triangle is right angled.

Proof :-

A right-angled triangle is a triangle whose one angle is 90° .

According to the question ,

The angle of a triangle are :-

• The first angle :- x

• The second angle :- 2x

• The third angle :- 3x

Angle sum property of a triangle :- The angle sum property of a triangle states that the sum of angles of a triangle is 180°.

Applying , The angle sum property of triangle.

∠A+∠B+∠C=180°

x+2x+3x=180°

6x=180°

x = $\cancel{\dfrac{180}{6}}$

x=30°

So,

The first angle :- x = 30°

The second angle :- 2x = 2 × 30 = 60°

The third angle :- 3x = 3 × 30 = 90°

We get one angle = 90°.It states that The triangle is a right angle trangle.

Hence Proved ✅

Answer 2

Step-by-step explanation:

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