Question

The angle of a triangle are in the ratio 1:2:3 then the angle of the triangle are.

Answer 1

Solution

Given :-

• The angle of a triangle are in the ratio 1:2:3

Find :-

• Angle of the triangle

Explanation

We Know,

Sum of all angle in triangle will be = 180°.

Let,

• First angle = x
• Second angle = 2x
• Third angle = 3x

So, Now add all angles

➡x + 2x + 3x = 180°

➡6x = 180°

➡x = 180/6

➡x = 30

Hence

• First angle will be(x) = 30°
• Second angle will be (2x) = 2 × 30 = 60°
• Third angle will be (3x) = 3 × 30 = 90°

_________________

Answer Verification

Sum of all angles in triangle

➡ 30° + 60° + 90° = 180°

➡180° = 180°

That's proved.

_________________

Answer 2

$\red\bigstar$ Answer:

The angles are :

• 30°
• 60°
• 90°

$\blue\bigstar$ Given:

• The angle of a triangle are in the ratio 1 : 2 : 3

$\pink\bigstar$To find:

• The angles of the triangle

$\green\bigstar$ Solution:

Let all the angles in form of x.

So, the angles are :

• x
• 2x
• 3x

$\because$We know that the sum of the angles in a triangle is 180°,

$\therefore$ x + 2x + 3x = 180°

(Angle Sum property of a triangle)

$\implies$ 3x + 3x = 180°

$\implies$ 6x = 180°

$\sf \: \implies \: x \: = \: \dfrac{{180}^{ \circ} }{6}$

$\sf \: \implies \: \boxed{\sf \: x \: = \: {30}^{ \circ} }$

$\therefore$ The angles are :

• x = 30°

• 2x = 2 × 30° = 60°

• 3x = 3 × 30° = 90°

$\red\bigstar$ Verification :

Here the angles are :

• 30°

• 60°

• 90°

$\because$ We know that the sum of angles in a triangle is 180°,

$\implies$ 30° + 60° + 90° = 180°

$\implies$ 180° = 180°

$\implies$ $\boxed{\tt LHS\: = \:RHS\:}$

Hence verified too!

$\blue\bigstar$ Concepts Used:

• Assumption of unknown angles

• Angle Sum property of a triangle

• Transposition Method

$\pink\bigstar$Extra - Information:

• The sum of all angles in a quadrilateral is 360°

• The sum of all angles in a Pentagon is 540°