Question

Three angles of the quadrilateral are in the ratio 1:2:3 and the sum of the greatest and smallest angle is 180 degree find the all angles are quadrilateral

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Answer 1

Answer:

Step-by-step explanation:

Ratio of 3 angles = 1:2:3

Let their common mutiple be 'x'

So, the three angles are x,2x,3x.

It is also given that sum of largest and the smallest angle is 180⁰.

So, let largest angle be 'A'

So, smallest angle is x

Angle sum of a quadrilateral is 360⁰ so A+x = 180⁰.........(given)

So it remains , 2x+3x=180⁰

5x=180

X=180/5

x=36⁰

So put the value of x in A+x=180⁰

A+36=180

A=180-36

A=144⁰

So, all the angles of quadrilateral are --

1. 36⁰

2. 144⁰

3. 2x = 2×36=72⁰

4. 3x= 3×36 = 108⁰

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Answer 2

Given :-

Ratio of the sides of the triangle = 1 : 2 : 3

The sum of the greatest and smallest angle = 180°

To Find :-

The first angle.

The second angle.

The third angle.

The fourth angle.

Solution :-

Consider the common ratio as 'x'. Then the angles would be x, 2x, 3x.

Given that,

Sum of the greatest and smallest angle = 180°

Making an equation,

x + 3x = 180

4x = 180

By transposing,

x = 180/4

x = 45°

Finding the three angles,

x = 45°

2x = 2 × 45 = 90°

3x = 3 × 45 = 135°

We know that,

Sum of a quadrilateral = 360°

Let the fourth angle be y.

Making an equation,

45 + 90 + 135 + y = 360

270 + y = 360

By transposing,

y = 360 - 270

y = 90°

Therefore, the four angles of quadrilateral are 45°, 90°, 90° and 135°.