Question

the ratio between the angles of a quadrilateral in 4:5:7 :8 find the angles of the quadrilateral​

Answer 1

Answer:

Let us angle is x.

4x : 5x : 7x :8x = 360

4x +5x+7x+8x =360

24x =360

x= 360/24

x=15

4x=60

5x=75

7x=105

8x=120

Thank you for your question.

I think so it may be helpful for you.

Answer 2

Given: ratio of angles of quadrilateral is 4:5:7:8.

To Find: the angles of the quadrilateral.

Solution

➸ According to Quadrilateral Angles Sum Property, the sum of all the four interior angles is 360 degrees.

✎ Let's assume that the ratio be x.

∠1 = 4x, ∠2 = 5x, ∠3 = 7x and ∠4 = 8x

ㅤ

$\sf \implies \angle1 + \angle2 + \angle3 + \angle4 = 360 \degree$

$\sf \implies \: 4x + 5x + 7x + 8x = 360 \degree$

$\sf \implies 9x + 15x = 360 \degree$

$\sf \implies \: 24x = 360 \degree$

$\sf \implies \: x = \dfrac{ \cancel{360}}{ \cancel{24} }$

$\sf \small{ \implies \: \boxed{ \boxed{ \purple{ \bf{x = 15 \degree}}}}}$

$\bf\therefore \underline{the \: anges \: will \: be}$

• ∠1 = 4x = 4(15) = 60°
• ∠2 = 5x = 5(15) = 75°
• ∠3 = 7x = 7(15) = 105°
• ∠4 = 8x = 8(15) = 120°

Hence, the angles of quadrilateral are 60°, 75°, 105° and 120°