Question

in the quadrilateral ABCD, angle BCD is equal to angle DAB and angle ABC is twice angle ADC. if angle ADC is 85° , find the measure of y

Answer 1

As ABC Is twice the angle ADC;

ABC IS 170°

BCD IS 52.5°

DAB IS 52.5°

Answer 2

Given  :   quadrilateral ABCD   , ∠BCD = ∠DAB   , ∠ABC = 2 ∠ADC  , ∠ADC = 85°

To Find : Measure of Y   ( external angle of B∠CD )

Solution:

∠ABC = 2 ∠ADC

∠ADC = 85°

=> ∠ABC =   2 x  85°

=> ∠ABC =  170°

∠BCD = ∠DAB  

In quadrilateral ABCD

∠ABC + ∠ADC + ∠BCD + ∠DAB   = 360°

∠BCD = ∠DAB    ,  ∠ABC =  170° , ∠ADC = 85°

=> 170° +  85° + ∠BCD + ∠BCD = 360°

=>  255° + 2∠BCD  = 360°

=> 2∠BCD  =105°

=>  ∠BCD  =52.5°

Measure of Y   ( external angle of B∠CD ) = 180° -  ∠BCD

=> Measure of Y   ( external angle of B∠CD ) = 180° -  52.5°

=> Measure of Y   ( external angle of B∠CD ) = 127.5°

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