Question

the angles for quadrilaterals are in the ratio 4:6:7:13 find all the angles of the quadrilaterals​

Answer 1

$\huge\mathcal\blue{Answer}$

angles of a quadrilateral 3:4:4:7

sum of angles in a quadrilateral =360 ∘

let the angles be 3x,4x,4x and 7x.

then, sum 360

3x+4x+4x+7x=360

18x=360

x=20

3x=60,4x=80,7x=140

∴ the angle of quadrilateral are 60∘ ,80 ∘ ,80 ∘ and 140 ∘

Answer 2

Question:-

the angles for quadrilaterals are in the ratio 4:6:7:13 find all the angles of the quadrilaterals

Answer:-

• The angles of quadrilateral are 48°,72°,84° and 156°

Solution:-

• Sum of angles = 360°
• Ratio = 4:6:7:13

Put x in the ratio :-

• 4x
• 6x
• 7x
• 13x

$\large{ \tt : \implies \: \: \: \: \: 4x + 6x + 7x + 13x = 360}$

$\large{ \tt : \implies \: \: \: \: \: 30x = 360}$

$\large{ \tt : \implies \: \: \: \: \: x = \frac{360}{30} }$

$\large{ \tt : \implies \: \: \: \: \: x = 12}$

• The value of x is 12°

____________________________

ANGLES ARE:-

• 4x = 4×12 = 48°
• 6x = 6×12 = 72°
• 7x = 7×12 = 84°
• 13x = 13×12 = 156°

_____________________________

Verification:-

$\large{ \tt : \implies \: \: \: \: \: 48 + 72 + 84 + 156 = 360}$

$\large{ \tt : \implies \: \: \: \: \: 360 = 360}$

HENCE VERIFIED!!