Math, asked by Anonymous, 10 months ago

in a quadrilateral, if it's four angles are in the ratio 5:2:4:7 then the sum if measures of the first two smaller angles is__________​

Answers

Answered by pandaXop
34

Sum = 120

Step-by-step explanation:

Given:

  • The four angles of a quadrilateral are in ratio 5:2:4:7.

To Find:

  • What is the sum of measure of first two smaller angles ?

Solution: Let x be the common in given ratio and angles of quadrilateral be ∠A , ∠B , ∠C and ∠D.

  • ∠A = 5x , ∠B = 2x
  • ∠C = 4x , ∠D = 7x

As we know that the sum of all interior angles of a quadrilateral is of 360°. Therefore,

\implies{\rm } A + B + C + D = 360°

\implies{\rm } 5x + 2x + 4x + 7x = 360°

\implies{\rm } 18x = 360°

\implies{\rm } x = 360/18

\implies{\rm } x = 20°

So,

➛ ∠A = 5x = 5(20) = 100°

➛ ∠B = 2x = 2(20) = 40°

➛ ∠C = 4x = 4(20) = 80°

➛ ∠D = 7x = 7(20) = 140°

Now, arranging the values of angles in ascending order:-

  • 40° , 80° , 100° , 140°

Here, First Smaller angle = 40° & Second smaller angles = 80°

Their sum = 40° + 80° = 120°

Hence, the sum of measure of first two smaller angles is 120° .

Answered by MisterIncredible
58

Given :-

In a quadrilateral ,

The four angles are in the ratio of 5 : 2 : 4 : 7

Required to find :-

  • Sum of the measures of the first two smaller angles ?

Conditions used :-

  • Sum of all angles in a quadrilateral = 360°

Solution :-

Given that :-

In a quadrilateral ,

The four angles are in the ratio of 5 : 2 : 4 : 7

we need to find the sum of the measures of first two smaller angles .

So,

Let consider ;

Ratio of the 4 angles = 5 : 2 : 4 : 7

So,

Let ,

  • 1st angle be 5x°

  • 2nd angle be 2x°

  • 3rd angle be 4x°

  • 4th angle be 7x°

According to the conditions of the quadrilateral ;

Sum of all four angles in a quadrilateral = 360°

5x° + 2x° + 4x° + 7x° = 360°

18x° = 360

x° = 360°/18

x° = 20°

So,

The actual measurements of the 4 angles are ;

  • 1st angle = 5x° = 5(20)° = 100°

  • 2nd angle = 2x° = 2(20)° = 40°

  • 3rd angle = 4x° = 4(20)° = 80°

  • 4th angle = 7x° = 7(20)° = 140°

From the above we can conclude that ;

The smallest angles are 2nd angle and 3rd angle

So,

Sum of first two smaller angles =

=> 1st angle + 2nd angle

=> 40° + 80°

=> 120°

Therefore,

Sum of first two smaller angles = 120°

Extra Knowledge :-

The different types of quadrilateral are ;

  • 1. Parallelogram

  • 2. Trapezium

  • 3. Rhombus

  • 4. Rectangle

  • 5. Square

  • 6. Kite

A quadrilateral is a 2nd geometrical figure which is bounded by 4 line segments .

The quadrilateral is also considered to be the 2nd polygon if we consider triangle as the 1st polygon .

Each quadrilateral has a unique property when compared to other quadrilaterals .

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