Question

The four angles of a quadrilateral are in the ratio 2:3:5:8. Find the greatest angle of the quadrilateral. *

Answer 1

Answer:

2x+5x+3x+8x =360 ( angle sum property of quadrilateral)

18x=360

x=20

2x=40

3x 60

5x 100

8 x 160

so greatest angle is 160

Answer 2

$\tt Sum \ of\ all\ angles \ in \ a \ quardrilateral = 360 \ Degree\\\\\tt Let \ the \ four\ angles\ of \ the \ quadrilateral\ be \ \bf{2x}\ , \bf{3x}\ ,\bf{5x}\ and\ \bf{8x}\ .\\\\\tt \longrightarrow 2x+3x+5x+8x = 360\\\\\tt \longrightarrow 18x=360\\\\\tt\longrightarrow x=360\div18\\\\\tt\longrightarrow x= \bf 20\\\\\tt\sf Greatest \ angle =8x=8\times20=\bf 160 \ Degree$

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