Question

The angles of a quadrilateral are in the ratio 4:5:3:6 . Find the difference between the largest and the smallest angles.

Answer 1

Answer :

• Largest angle is 120⁰
• Smallest angle is 60⁰

Given :

• The angles of a quadrilateral are in the ratio 4:5:3:6

To find :

• The difference between the largest and the smallest angles

Solution :

Given

• The angles of a quadrilateral are in the ratio 4:5:3:6

• Let the angles be 4x , 5x , 3x and 6x

We know that

• Sum of all angles of a quadrilateral is equal to 360⁰

↦ 4x + 5x + 3x + 6x = 360⁰

↦ 9x + 9x = 360⁰

↦ 18x = 360⁰

↦ x = 360/18

↦ x = 20

Finding the largest and smallest angles :

↦ 4x

↦ 4(20)

↦ 80⁰

↦ 5x

↦ 5(2)

↦ 100⁰

↦ 3x

↦ 3(20)

↦ 60⁰

↦ 6x

↦ 6(20)

↦ 120⁰

• Largest angle is 120⁰
• Smallest angle is 60⁰

Answer 2

✰ Given :-

The angles of a quadrilateral are in the ratio 4:5:3:6.

$\:$

✰ To Find :-

The difference between the largest and the smallest angles.

$\:$

✰ Used Formula :-

$\red \star \: \colorbox{lime}{\bf Sum of all angles = 360°}$

$\:$

✰ Solution :-

In quadrilateral,

Sum of all angles = 360°

Here,

The angles are in ratio.

$\bf \red⇢ \: 4x + 5x + 3x + 6x = 360 \degree$

$\bf \red⇢ \: 18x = 360 \degree$

$\displaystyle \bf \red⇢ \: x = \cancel\frac{360}{18} = 20$

$\bf\red⇢ \: \boxed{ \large \bf \colorbox{yellow}{x = 20 \degree}}$

$\bf \purple⇝ \: 4x = 20\times 4 = 80$

$\bf \purple⇝ \: 5x = 20\times 5 = 100$

$\bf \purple⇝ \: 3x = 20\times 3= 60$

$\bf \purple⇝ \: 6x = 20\times 6 = 120$

$\:$

✰ Proof :-

$\bf \red⇢ \: 80\degree+ 100 \degree+ 60\degree + 120\degree = 360 \degree$

$\bf \red⇢ \: 360 \degree = 360 \degree$

$\:$

Here,

The largest angle is 120°

And the smallest angle is 60°

The difference between the largest and the smallest angle is 120°-60° = 60°