Question

Calculate all the angles of a quadrilateral if they are in the ratio 2:5:4:1.​

Answer 1

As the angles are in the ratio 2:5:4:1, they can be written as-

2x, 5x, 4x, and x

Now, as the sum of the angles of a quadrilateral is 360°,

2x + 5x + 4x + x = 360°

Or, x = 30°

Now, all the angles will be,

2x =2 × 30° = 60°

5x = 5 × 30° = 150°

4x = 4 × 30° = 120°

x = 30°

Answer 2

Required Answer :

The four angles of quadrilateral are 60°, 150°, 120° and 30°.

Given :

Ratio of the angles of quadrilateral = 2 : 5 : 4 : 1

To find :

All the angles of quadrilateral

Concept :

To find all the angles of quadrilateral which are given in the ratio. Firstly, we will assume the angles according to the ratio. Then by using the following formula we will calculate all the angles of quadrilateral.

Formula to calculate the sum of angles of a polygon :-

• Sum of interior angles of polygon = (2n - 4) × 90°

where,

• n = number of sides

Solution :

Let,

• First angle = 2x
• Second angle = 5x
• Third angle = 4x
• Fourth angle = 1x

A quadrilateral has 4 sides, angles.

So, number of sides (n) = 4

→ 2x + 5x + 4x + 1x = (2 × 4 - 4) × 90°

→ 12x = (8 - 4) × 90°

→ 12x = 4 × 90°

→ 12x = 360°

→ x = 360°/12

→ x = 30°

Substituting the value of x :-

→ First angle = 2x = 2(30°) = 60°

→ Second angle = 5x = 5(30°) = 150°

→ Third angle = 4x = 4(30°) = 120°

→ Fourth angle = 1x = 30°