Solve it quickly
Q.15. In the given figure. prove that:
$\angle ADC=\angle A+\angle B+\angle C$.

Dear Student,

Please find below the solution to the asked query:

We have our diagram , As :

Here we have join BD .

We know : Exterior Angle Theorem ,  The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle. So

$\angle$ ADB  = $\angle$ C  +  $\angle$ DBC                                        --- ( 1 )

And

$\angle$ CDB =  $\angle$ A + $\angle$ DBA                                         --- ( 2 )

Now we add equation 1 and 2 and get :

$\angle$ ADB + $\angle$ CDB =  $\angle$ A  + ( $\angle$ DBC + $\angle$ DBA ) + $\angle$ C  , From given diagram we get :

$\angle$ ADC =  $\angle$ A  +  $\angle$ B +  $\angle$ C                                           ( Hence proved )


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