Question

If the angles of a quadrilateral are in the ratio 2 : 3 : 6 : 7, then the difference of the largest and smallest angle is

Answer 1

Given:

• angles of a quadrilateral are in the ratio 2:3:6:7

To Find:

difference of the largest and smallest angle

Solution:

Let the angles of the quadrilateral be :

2x, 3x, 6x and 7x

We Know That:

$\boxed{\underline{\purple{\sf{sum\:of\: angles\:of\:a\:quadrilateral\:= 360°}}}}$

$\sf{\implies 2x + 3x + 6x + 7x = 360\degree}$

$\sf{\implies 18x = 360\degree}$

$\sf{\implies x = \frac{360}{18}}$

$\sf{\implies x = 20}$

Now,

• $\sf{ the\:largest\:angle\:= 7x = 7 \times 20 = 140\degree}$

• $\sf{ the\:smallest\:angle\:= 2x = 2 \times 20 = 40\degree}$

therefore,

difference of the largest and smallest angle of the quadrilateral

$\sf{\implies 140\degree - 40\degree}$

$\sf\red{\implies 100\degree}$

Hence,

difference of the largest and the smallest angle is 100°

Answer 2

$\huge{ \boxed{ \pink{ \sf{Question:-}}}}$

If the angles of a quadrilateral are in the ratio 2 : 3 : 6 : 7, then the difference of the largest and smallest angle is.

To find:-

• The difference between the largest and the smallest angle.

Hint:-

• To find the difference we will first find the measures of all angles.

We know that,

• The sum of all angles of a quadrilateral is 360°.

Let the measure of angles be:-

• 2x
• 3x
• 6x
• 7x

$\huge{ \underline{ \boxed{ \bf{Solution : - }}}}$

$\red{⇴} \mathfrak{2x + 3x + 6x + 7x = 360 \degree} \:$

$\pink{⇴} \: \bf18x = 360 \degree$

$\green{⇴} \bf{x = \frac{360}{180} }$

$\blue{⇴} \sf{20 \degree}$

Therefore the value of x is 20°

So the measures of angles:-

⇴ 2x=2×20°=40°

⇴ 3x=3×20°=60°

⇴6x=6×20°=120°

⇴ 7x=7×20°=140°

$\boxed{ \underline{ \mathfrak{ \green{Therefore \: the \: measure \: of \: the \: largest \: angle \: is \: 140° \: and \: the \: smallest \: is \: 40°}}}}$

Now we will find the difference between the largest and smallest angle.

$\large{ \red{⇝}} \small\bf{140 \degree - 40 \degree}$

$\large{ \pink{⇝}} \small 100 \degree$

$\boxed{ \underline{ \red{ \mathfrak{Therefore \: the \: difference \: between \: the \: largest \: and \: the \: smallest \: angles \: is \: 100°.}}}}$