Question

The angles of a quadrilateral are in the ratio 3:5:4:3 find the angles​

Answer 1

$\bf{\underline{Question:-}}$

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

$\bf{\underline{QUADRILATERAL\: PROPERTY:-}}$

• Sum of 4 angles of quadrilateral = 360°

$\bf{\underline{</u></strong><strong><u>S</u></strong><strong><u>o</u></strong><strong><u>l</u></strong><strong><u>u</u></strong><strong><u>t</u></strong><strong><u>i</u></strong><strong><u>o</u></strong><strong><u>n</u></strong><strong><u>:-}}$

Let,

• All the ratios be = x

So,

• 3 = 3x
• 5 = 5x
• 4 = 4x
• 3 = 3x

† ACCORDING TO QUADRILATERAL PROPERTY †

→ 3x + 5x + 4x + 3x = 360°

→ 8x + 7x = 360°

→ 15x = 360°

→ x = 360/15

→ x = 24

$\bf{\underline{</strong><strong>H</strong><strong>e</strong><strong>n</strong><strong>c</strong><strong>e</strong><strong>:</strong><strong>-}}$

• 1st angle = 3x = 3 × 24 = 72°
• 2nd angle = 5x = 5 × 24 = 120°
• 3rd angle = 4x = 4 × 24 = 96°
• 4th angle = 3x = 3 × 24 = 72°

$\bf{\underline{VERIFICATION:-}}$

BY THE PROPERTY

• Sum of 4 angle of quadrilateral= 360°

→ 72 + 120 + 96 + 72 = 360°

→ 192 + 168 = 360°

→ 360° = 360°

Verified

Answer 2

Answer:

$\bigstar{\bold{First\:angle\:=\:72^{o} }}$

$\bigstar{\bold{Second\:angle\:=\:120^{o} }}$

$\bigstar{\bold{Third\:angle\:=\:96^{o} }}$

$\bigstar{\bold{Fourth\:angle\:=\:72^{o} }}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

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

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• All the angles of the quadrilateral

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let the first angle be 3x

→ Let the second angle be 5x

→ Let the third angle be 4x

→ Let the fourth anle be 3x

→ The sum of all the angles in a quadrilateral is 360°

→ Hence,

  3x + 5x + 4x + 3x = 360°

  15x = 360°

   x = 24

→ ∴ First angle = 3x = 3 × 24

  $\boxed{\bold{First\:angle\:=\:72^{o} }}$

→ ∴ Second angle = 5x = 5 × 24

  $\boxed{\bold{Second\:angle\:=\:120^{o} }}$

→ ∴ Third angle = 4x = 4 × 24

   $\boxed{\bold{Third\:angle\:=\:96^{o}}}$

→ ∴ Fourth angle = 3x = 3 × 24

   $\boxed{\bold{Fourth\:angle\:=\:72^{o} }}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The sum of interior angles of a polygon is given by the formula

   Sum of angles = (n-2)180

   where n is the number of sides of the polygon.