Question

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

Answer 1

Given :-

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

To find :-

The all angles of a quadilateral .

Solution:-

The sum of the angle of a quadilateral is 360°.

Let the angles in ratio be 3x , 5x , 9x and 13x .

A/Q

→$3x + 5x + 9x + 13x = 360^{\circ}$

→$30 x = 360$

→$x = \dfrac{360}{30}$

→$\huge \boxed{x = 12^{\circ} }$

hence, The angles of qudialiteral are :-

→3x = 3 × 12 = 36°

→5x = 5 × 12 = 60°

→9x = 9 × 12 = 108°

→13x = 13 × 12 = 156°

Verification:-

Add all the angles we get 360°

→ 36 + 60 + 108 + 156 = 360°

→ 360° = 360° verified..

Answer 2

$\underline{\underline\mathfrak{Given : }}$

Angles are in ratio 3 : 5 : 9 : 13

$\underline{ \underline \mathfrak{to \: find}} \: : angles \: of \: a \: quadrilateral$

$\underline{ \underline \mathfrak{Solution}}$

Let the angles be x

$\therefore \: 3x : 5x : 9x : 13x$

The sum of interior angle of a quadrilateral is 360 °

$\implies \: 3x + 5x + 9x + 13x = 360 \degree$

$\implies \: 30x = 360 \degree$

$\implies \: x = \dfrac{ \cancel{360}}{ \cancel{30} }$

$\large{\boxed{ \implies \: x = 12 \degree}}$

$\therefore \: each \: angles \: are$

$3 x = 3 \times 12 = 36 \degree$

$5x = 5 \times 12 = 60 \degree$

$9x = 9 \times 12 = 108 \degree$

$13x = 13 \times 12 = 156 \degree$