The internal angles of quadrilateral are in A.P. and their common difference is `10^@`. Find them.

Explanation

Let the angles of the quadrilateral be
`a,a+10^(@),a+20^(@),a+30^(@) " " `(`:.` common difference is `10^(@)`)
`:. a+(a+10^(@))+(a+20^(@))+(a+30^(@))=360^(@)`
`rArr 4a+60^(@)=360^(@)`
`rArr 4a=300^(@)`
`rArr a=75^(@)`
`:. a+10^(@)=75^(@)+10^(@)=85^(@)`
`a+20^(@)=75^(@)+20^(@)=95^(@)`
`a+30^(@)=75^(@)+30^(@)=105^(@)`
Hence, the angles are `75^(@), 85^(@), 95^(@), 105^(@)`.
Alternative Method :
Let the four angles of a quadrilateral are
`a-3d,a-d,a+d and a+3d`
`:.` Here common difference is 2d (remember)
`:. (a-3d)+(a-d)+(a+d)+(a+3d)=360^(@)`
`rArr 4a=360^(@) rArr a=90^(@)`
common difference is given to be `10^(@)`
`:. "i.e.," 2d=10^(@) rArr d=5^(@)`
`:.` Four angles are `a-3d=90^(@)-3(5^(@))=75^(@)`,
`a-d=90^(@)-5^(@)=85^(@)`,
`a+d=90^(@)+5^(@)=95^(@)`,
`a+3d=90^(@)+3(5^(@))=105^(@)`.