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Given ratio of the angles of a quadrilateral is 7:3:4:6 Let the angles be 7x,3x,4x,6x sum of the angles in a quadrilateral is 360° ⇒7x+3x+4x+6x = 360° ⇒20x=360° ⇒x=360/20 ⇒x = 18° Therefore the angles are 7(18),3(18),4(18),6(18) ⇒126°,54°,72°,108° EFGH is a cyclic quadrilateral .

The angles of the quadrilateral are 7x,3x,4x and 6x sum of all angles in a quadrilateral is 360 therefore, 7x+3x+4x+6x=360 20x=360 x=18degrees the angles are therefore 7(18),3(18),4(18),6(18) =126,54,72,108

so...since the opposite angles are supplementery..that is, 126+54=180 108+72=180 therefore it is a cyclic quadrilateral