The angles of a quadrilateral are in AP the ratio between the product of 1st and 4th to product of 3rd and 2nd is27:28 done the angles of quadrilateral
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let the first angle be a
therefore second angle =a+d
third angle=a+2d
fourth angle=a+3d
the product of first and fourth =a*(a+3d)
=a²+3ad
the product of second and third=(a+d)(a+2d)
=a²+2ad+ad+2d²
=a²+3ad+d²
therefore
(a²+3ad)/(a²+3ad+d²)=27/28
(a²+3ad+d²)/(a²+3ad)=28/27
a²+3ad/a²+3ad)+(d²/a²+3ad)
therefore second angle =a+d
third angle=a+2d
fourth angle=a+3d
the product of first and fourth =a*(a+3d)
=a²+3ad
the product of second and third=(a+d)(a+2d)
=a²+2ad+ad+2d²
=a²+3ad+d²
therefore
(a²+3ad)/(a²+3ad+d²)=27/28
(a²+3ad+d²)/(a²+3ad)=28/27
a²+3ad/a²+3ad)+(d²/a²+3ad)
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