Question

in the figure ABCD is a cyclic quadrilateral in which ab is produced to F and BE parallel DC if angle FBEis equal to 20 degree and Angle DAB = 95 degree find angle ADC

Answer 1

Abcd is cyclic quad.
So <DAB+<BCD=180
<Bcd=85
BE is parallel to DC so
<Dcb=<Cbe (alternate angles) = 85
So angle cbf = 20+85=105
According to the properties of a cyclic quad.
The ex. Angle is equal to its interior opp. Angles
So angle ADC = 105

Answer 2

Angle ADC is 105° .

Step 1: Find the angle ADC.

Given- ABCD is a cyclic quadrilateral, BE║DC, ∠FBE=20° , ∠DAB=95°

Sum of opposite angles of a cyclic quadrilateral is 180° .

∠DAB+∠BCD=180°

95°+∠BCD=180°  

∠BCD=180° -95°

           =85°

As we know BE║DC,

∠CBE=∠BCD                                        (∵alternate interior angle)

          =85°                                      

∠CBF=∠CBE+∠EBF

          =105°

Now , ∠ABC+∠CBF=180°                                             (∵linear pair)

and ∠ABC+∠ADC=180°                  (∵opposite angles of cyclic quadrilateral)

Hence, ∠ABC+∠ADC=∠ABC+∠CBF

∠ADC=∠CBF

∠ADC=105°                                                             (∵∠CBF = 105°)