Question

the angles of a quadrilateral are in the ratio 1:3:5:6 find its greatest angle​

Answer 1

Step-by-step explanation:

Answer in full explanation:-

_______________________

1x +3x + 5x + 6x = 360

15x = 360

x = 360/15

x = 24

6x = 24 × 6

= 144

Answer 2

$\large {\pmb{\mathfrak{☆ \: Given:}}}$

The angles of a quadrilateral are in the ratio of 1:3:5:6.

$\large {\pmb{\mathfrak{☆ \: \: To \: find:}}}$

We have to find the greatest angle in the quadrilateral.

$\large {\pmb{\mathfrak{☆ \: \: Solution: }}}$

We know that, sum of all the angles in a quadrilateral = 360°.

Let the unknown constant be x.

$\sf :\implies x+3x+5x+6x=360\degree$

$\sf :\implies 15x=360\degree$

$\sf :\implies x= \dfrac{360\degree}{15}$

$\boxed{\pmb{\sf {\therefore \: x=24\degree}}}$

Now, substituting x = 24° in the ratios :

$\sf :\implies \measuredangle1: \pmb{\sf x=24\degree}$

$\sf :\implies \measuredangle2:{\pmb{\sf{3x=3(24\degree)=72\degree}}}$

$\sf :\implies \measuredangle3:{\pmb{\sf{5x=5(24\degree)=120 \degree}}}$

$\sf :\implies \measuredangle4:{\pmb{\sf{6(24\degree)=144 \degree}}}$

$\boxed{\pmb{\sf{\therefore \: Greatest \: angle =144\degree}}}$

$\large {\pmb{\mathfrak{☆ \: \: Verification:}}}$

Let's verify whether the angles add upto 360° or not :

$\sf :\implies x+3x+5x+6x=360\degree$

$\sf :\implies 24\degree+3(24\degree)+5(24\degree)+6(24\degree)=360$

$\sf :\implies 24\degree+72\degree+120 \degree + 144 \degree = 360 \degree$

$\sf:\implies 96\degree+264 \degree = 360 \degree$

$\sf :\implies {360\degree=360\degree}$

$\boxed{\pmb{\sf{Hence, ~ verified!}}}$