Question

The angle of a quadrilateral are in the 1:2:3:4.Find all the angles of the quadrilateral

Answer 1

Let the common multiple be x ..

Let the angle of quadrilateral be 1x , 2x , 3x , 4x

Angle sum property of a quadrilateral = 360°

So ,

1x + 2x + 3x + 4x = 360°

10x = 360°

x = 360/10

x = 36 °

Now , the angles of the quadrilateral are :

a ) 1x

--> 1 × 36

--> 36°

b) 2x

--> 2 × 36

--> 72°

c) 3x

--> 3 × 36

--> 108°

d) 4x

--> 4 × 36

--> 144°

So all the angles of the quadrilateral are 36 , 72 , 108 , 144

I hope it helps u dear friend ^_^♡♡

Answer 2

Given that,

• The angle of a Quadrilateral are in the 1:2:3:4.

☯ Let the angles of the Quadrilateral be x, 2x, 3x 4x.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{As \ We \ know \ that,}}}$⠀

• Sum of the measures of all angles of triangle is 360°.⠀⠀⠀⠀

⠀⠀⠀

Therefore,⠀

⠀⠀⠀

$:\implies\sf x + 2x + 3x + 4x = 360 \\\\\\:\implies\sf 10x = 360 \\\\\\:\implies\sf x = \cancel\dfrac{360}{10}\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 36^{\circ}}}}}} \ \bigstar$

⠀⠀⠀

$\underline{\textsf{ Angles of Quadrilateral are :}}$

⠀⠀⠀

• First angle, (x) = 36°
• Second angle, (2x) = 2(36) = 72°
• Third angle, (3x) = 3(36) = 108°
• Fourth angle, (4x) = 4(36) = 144°

⠀⠀⠀

$\therefore$ Hence, Required angles of the Quadrilateral are 36°, 72°, 108° and 144°.