Question

In a quadrilateral , the angles are in a ratio 2 : 4 : 5 : 7. Find the difference between the greatest and the smallest angle.
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Answer 1

Answer:

Given :-

• Ratio of angles = 2:4:5:7

To Find :-

Difference between largest and smallest

Solution :-

So, for finding the difference between the smallest and largest angle we have to find the angles

Let the angle be x

As we know that sum of all sides in a quadrilateral is 360⁰.

$\sf: \implies2x + 4x + 5x + 7x = 360$

$\sf : \implies \: 6x + 12x = 360$

$\sf : \implies \: 18x = 360$

$\sf : \implies \: x = \dfrac{360}{18}$

$\sf : \implies \: x = 20$

Now,

Let's find angle

$\sf : \mapsto2x = 2(20) = 40$

$\sf : \mapsto \: 4x = 4(20) = 80$

$\sf : \mapsto \: 5x = 5(20) = 100$

$\sf : \mapsto \: 7x = 7(20) = 140$

Now,

Let's find the difference between largest and smallest one

$\sf : \rightarrow \: Difference \: = 140 - 40$

$\sf : \rightarrow \: Difference = 100$

Answer 2

Answer:

Given :-

Ratio of angles = 2:4:5:7

To Find :-

Difference between largest and smallest

Solution :-

So, for finding the difference between the smallest and largest angle we have to find the angles

Let the angle be x

As we know that sum of all sides in a quadrilateral is 360⁰.

\sf: \implies2x + 4x + 5x + 7x = 360:⟹2x+4x+5x+7x=360

\sf : \implies \: 6x + 12x = 360:⟹6x+12x=360

\sf : \implies \: 18x = 360:⟹18x=360

\sf : \implies \: x = \dfrac{360}{18}:⟹x=

18

360

\sf : \implies \: x = 20:⟹x=20

Now,

Let's find angle

\sf : \mapsto2x = 2(20) = 40:↦2x=2(20)=40

\sf : \mapsto \: 4x = 4(20) = 80:↦4x=4(20)=80

\sf : \mapsto \: 5x = 5(20) = 100:↦5x=5(20)=100

\sf : \mapsto \: 7x = 7(20) = 140:↦7x=7(20)=140

Now,

Let's find the difference between largest and smallest one

\sf : \rightarrow \: Difference \: = 140 - 40:→Difference=140−40

\sf : \rightarrow \: Difference = 100:→Difference=100