Question

if angles of a triangle are in the ratio 1:2:3 ,find the value of each angle​

Answer 1

Given

• Ratio of angles of triangle = 1 : 2 : 3

To find

• Value of each angle of the triangle

Solution

Let the angles of triangle be x, 2x and 3x.

As we know that,

Sum of angles of triangle = 180°

So, we will add all the angles and keep it equal to 180°.

⟼ x + 2x + 3x = 180°

⟼ 6x = 180°

⟼ x = 180°/6

⟼ x = 30°

The value of x = 30°.

Therefore, each angle of triangle :-

• First angle = x = 30°
• Second angle = 2x = 2 × 30° = 60°
• Third angle = 3x = 3 × 30° = 90°

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Let's verify :-

If the sum of these angles will be equal to 180°. Then their value is right.

⟼ 30° + 60° + 90°

⟼ 180°

Hence, verified.

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Know More :-

More about triangles :-

Isosceles triangle -

• In this triangle two sides are equal to each other and the third side is unequal.

Equilateral triangle -

• In this triangle all sides are equal to each and their angles are also equal.

Scalene triangle -

• In this triangle are sides are unequal.

Some formulae -

• Area of triangle = 1/2 × base × height
• Semi perimeter = (a + b + c)/2
• Perimeter = Sum of all sides.

Answer 2

$\huge\mathbb{\purple{ANSWER}}$

Angles of a triangle are in the ratio 1:2:3

Let the angles be x, 2x, 3x

Sum of all angles of triangles = 180°

↣x + 2x + 3x = 180°

↣6x = 180°

↣x = 180/6

↣x = 30°

Answer:

• x = 30°
• 2x = 2(30)° = 60°
• 3x = 3(30)° = 90°

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Equilateral Triangle

The Equilateral Triangles have the following properties (in addition to the properties above for all triangles):

• Three straight sides of equal length
• Three angles, all equal to 60°
• Three lines of symmetry

Isosceles Triangle

The Isosceles Triangles have the following properties:

• Two sides of equal length
• Two equal angles
• One line of symmetry

Scalene Triangle

Scalene triangles have the following properties

• No sides of equal length
• No equal angles
• No lines of symmetry

Acute triangles

Acute triangles have all acute angles (angles less than 90°). It is possible to have an acute triangle which is also an isosceles triangle – these are called acute isosceles triangles.

Right triangles

The Right Triangles (right-angled triangles) have one right angle (equal to 90°).It is possible to have a right isosceles triangle – a triangle with a right angle and two equal sides.

Obtuse triangles

Obtuse triangles have one obtuse angle (angle which is greater than 90°). It is possible to have a obtuse isosceles triangle – a triangle with an obtuse angle and two equal sides.

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