Question

If the angles of a quadrilateral are x, x + 30°, x + 60 and 4x then the difference between greatest angle and the smallest is
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Answer 1

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▪Given :-

The internal angles of a quadrilateral are

x, x + 30°, x + 60 and 4x

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▪To Calculate :-

The difference between greatest angle and the smallest angle.

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▪Key Concept :-

☆《Angle Sum Property》

The sum of internal angles of any quadrilateral is

360°.

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▪Solution :-

As

1st angle = x

2nd angle = x + 30°

3rd angle = x + 60°

4th angle = 4x

According to Angle Sum Property :-

x + x + 30° + x + 60° + 4x = 360°

⟹ 7x + 90° = 360°

⟹ 7x = 270°

$\implies\boxed{\underline{\red{ \large \mathfrak{x = \bf \frac{270}{7} }}}}$

So,

1st angle = 270°/7

2nd angle =270°/7+ 30° = 480°/7

3rd angle = 270°/7 + 60° = 690°/7

4th angle = 4 × 270°/7 = 1080°/7

Now,

The difference between greatest angle and the smallest angle = 1080°/7 - 270°/7

= 810°/7

$\red{\Large\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required}}\\\red{ \huge\mathfrak{ \text{ A}nswer.}}$

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Answer 2

Given :-

Angle are x, x + 30, x + 60 and 4x

To Find :-

Angle

Solution :-

Sum of all angle is 360⁰

x + x + 30 + x + 60 + 4x = 360

7x + 90 = 360

7x = 360 - 90

7x = 270

x = 270/7

Now finding the difference

Largest angle = 4x

Smallest angle = x

Difference = 4 × (270/7) - 270/7

Difference = 1080/7 - 270/7

Difference = 810/7