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
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Answered by
101
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
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
Answered by
16
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°)
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