Question

In the adjoining figure,DO and CO are the bisectors of angle ADC and angle BCD respectively.If angle ADC= angle BDC = 60°, and angle DAB = 100°, find the measures of angle DOC,angle ADC and angle ABC​

Answer 1

Step-by-step explanation:

Given,

∠BAD=70

∠ABD=56

∠ADC=72

ABCD is a cyclic quadrilateral.We know, that sum of opposite angles of a cyclic quadrilateral is 180.

Therefore,

∠BAD+∠BCD=180

=>∠BCD=180−70

=110 (ii)

∠ADC+∠ABC=180

=>72+∠ABD+∠DBC=180

=>72+56+∠CBD=180

=>∠CBD=180−128

=52

In △BCD,

∠BCD+∠DBC+∠BDC=180

=>110+52+∠BDC=180

=>∠BDC=18 (i)