Question

ABCD is a cyclic quadrilateral .if AB || DC. angle DAB = 80° .Find angle ABC

Answer 1

Given ABCD is a cyclic quadrilateral.

and AB // DC

i ) <DAB + <BCD = 180°

[Pair of Opposite angles are

supplementary ]

=> 80° + <BCD = 180°

=> <BCD = 180° - 80° = 100°

ii ) AB // DC , Transversal BC

<ABC + <BCD = 180°

[ Sum of interior angles same side

of the transversal ]

=> <ABC + 100° = 180°

=> <ABC = 180° - 100° = 80°

•••••

Answer 2

given
angle DAB = 80 degree
solution
opposite angles of a cyclic quadrilateral are supplementary
angle DCB +angle DAB = 180
angleDCB = 100
all angles of a quadrilateral is 360
angle DAB + angle DCB + angle ADC + angle ABC = 360
80 +100 +angle ADC +angle ABC =360
180 + angle ADC +angle ABC =360
angle ADC + Angle ABC= 360 - 180
ADC + ABC = 180
ABC= 90