Question

The angles of quadrilateral are in the ratio 3:5:9:13.find all other
angles of the quadrilateral.​

Answer 1

${\huge {\bf {\underbrace {Question}}}}$

The angles of quadrilateral are in the ratio 3:5:9:13.find all other

angles of the quadrilateral.

${\huge {\bf {\underbrace {Answer}}}}$

Given:-

• The angles of the quadrilateral are in the ratio 3:5:9:13

To Find:-

• All angles of the quadrilateral.

Solution:-

Let, the angles in the ratio 3:5:9:13 be ∠A, ∠B, ∠C and ∠D

Let,

∠A = 3x

∠B = 5x

∠C = 9x

∠D = 13x

Where, x is any number.

We know that,

${\boxed{\bf{\pink{Sum\: of\: all\: angles\: of\: a\: quadrilateral\: is\: 360°}}}}$

${\sf {⟹∠A + ∠B + ∠C + ∠D = 360°}}$ (Angle sum property of quadrilateral)

${\sf {⟹3x + 5x + 9x + 13x = 360°}}$

${\sf {⟹30x = 360°}}$

$\large {\sf {⟹\frac{360}{30}}}$

${\sf {⟹}}$${\sf {\boxed {\green {x = 12°}}}}$

⠀⠀⠀

Hence, the angles are

${\sf {⟹}}$ ${\sf {∠A = 3x = 3 × 12 = 36°}}$

${\sf {⟹}}$ ${\sf {∠B = 5x = 5 × 12 = 60°}}$

${\sf {⟹}}$ ${\sf {∠C = 9x = 9 × 12 = 108°}}$

${\sf {⟹}}$ ${\sf {∠D = 13x = 13 × 12 = 156°}}$

Answer 2

Answer:

The angles of quadrilateral are in the ratio 3:5:9:13.find all other

angles of the quadrilateral.

{\huge {\bf {\underbrace {Answer}}}}

Answer

Given:-

The angles of the quadrilateral are in the ratio 3:5:9:13

To Find:-

All angles of the quadrilateral.

Solution:-

Let, the angles in the ratio 3:5:9:13 be ∠A, ∠B, ∠C and ∠D

Let,

∠A = 3x

∠B = 5x

∠C = 9x

∠D = 13x

Where, x is any number.

We know that,

{\boxed{\bf{\pink{Sum\: of\: all\: angles\: of\: a\: quadrilateral\: is\: 360°}}}}

Sumofallanglesofaquadrilateralis360°

{\sf {⟹∠A + ∠B + ∠C + ∠D = 360°}}⟹∠A+∠B+∠C+∠D=360° (Angle sum property of quadrilateral)

{\sf {⟹3x + 5x + 9x + 13x = 360°}}⟹3x+5x+9x+13x=360°

{\sf {⟹30x = 360°}}⟹30x=360°

\large {\sf {⟹\frac{360}{30}}}⟹

30

360

{\sf {⟹}}⟹ {\sf {\boxed {\green {x = 12°}}}}

x=12°

⠀⠀⠀

Hence, the angles are

{\sf {⟹}}⟹ {\sf {∠A = 3x = 3 × 12 = 36°}}∠A=3x=3×12=36°

{\sf {⟹}}⟹ {\sf {∠B = 5x = 5 × 12 = 60°}}∠B=5x=5×12=60°

{\sf {⟹}}⟹ {\sf {∠C = 9x = 9 × 12 = 108°}}∠C=9x=9×12=108°

{\sf {⟹}}⟹ {\sf {∠D = 13x = 13 × 12 = 156°}}∠D=13x=13×12=156°