The internal angles of quadrilateral are in A.P. and their common diff

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

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