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Question

In the figure, BAD=4DBA, what is the measure of ABC and x in degrees?


  1. 15, 45
  2. 60, 45
  3. 30, 60
  4. 60, 30


Solution

The correct option is B 60, 45
GivenBAD=4DBAADB=105 ,BCD=60 

In ΔADB,
DBA+ADB+BAD=180                           [Angle sum property]DBA+105+4DBA=180                105+5DBA=180                             5DBA=180105                               DBA=755                                                 =15 In ΔDBC,     DBC+BCD+CDB=180                          [Angle sum property][CDB+BDA=180                So,CDB=180 105                                    =75 ]        x+60+75=180                            x=180 135                                   =45In ΔABC,ABC=DBA+DBC                 =15 +x                  =15 +45            B=60

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