If the angles of a quadrilateral are in A.P. | vedclass

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(B) Let the four angles of the quadrilateral be $x, x+10^o, x+20^o,$ and $x+30^o$ in $A.P.$The sum of the interior angles of a quadrilateral is $360^o

Vedclass · Accepted Answer

$75^o, 85^o, 95^o, 105^o$

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(B) Let the four angles of the quadrilateral be $x, x+10^o, x+20^o,$ and $x+30^o$ in $A.P.$The sum of the interior angles of a quadrilateral is $360^o$.Therefore,$x + (x+10^o) + (x+20^o) + (x+30^o) = 360^o$.$4x + 60^o = 360^o$.$4x = 300^o$.$x = 75^o$.The angles are $75^o, 75^o+10^o=85^o, 75^o+20^o=95^o,$ and $75^o+30^o=105^o$.Thus,the angles are $75^o, 85^o, 95^o,$ and $105^o$.

If the angles of a quadrilateral are in $A.P.$ whose common difference is $10^o$,then the angles of the quadrilateral are

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