Question

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

Answer 1

Answer:

Sum of all angles in quadrilateral is 180.

Then 3x+5x+9x+13x=180

30x=180

x=6

The angels of quadrilateral is 3(6),5(6),9(6),13(6)

i.e..., 18,30,54,78

hope it helps u...

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Answer 2

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

☯ Given :

Angles of quadrilateral are in ratio 3:5:9:13.

$\rule{200}{1}$

☯ To Find :

We have to find all the angles of the quadrilateral.

$\rule{200}{1}$

☯ Solution :

Let the angle of quadrilateral be x. so,

First angle = 3x

Second angle = 5x

Third angle = 9x

Fourth angle = 13x

We know that,

$\small{\star{\boxed{\sf{Sum \: of \: angles \: of \: quadrilateral = 360^{\circ}}}}}$

✝ Putting Values

$\sf{\rightarrow 3x + 5x + 9x + 13x = 360} \\ \\ \sf{\rightarrow 8x + 22x = 360} \\ \\ \sf{\rightarrow 30x = 360} \\ \\ \sf{\rightarrow 30x = 360} \\ \\ \sf{\rightarrow x = \frac{\cancel{360}}{\cancel{30}}} \\ \\ \sf{\rightarrow x = 12}$

So,

First angle = 3x = 3(12) = 36°

Second angle = 5x = 5(12) = 60°

Third Angle = 9x = 9(12) = 108°

Fourth angle = 13x = 13(12) = 156°

$\rule{200}{2}$

☯ Veeification :

For verification we will add all the angles and put them equal to 360°.

$\sf{\rightarrow 36^{\circ} + 60^{\circ} + 108^{\circ} + 156^{\circ} = 360^{\circ}} \\ \\ \sf{\rightarrow 96^{\circ} + 264^{\circ} = 360^{\circ}} \\ \\ \sf{\rightarrow 360^{\circ} = 360^{\circ}}$

$\sf{\therefore \: L.H.S = R.H.S}$

★ Hence Verified