ABCD is a rhombus and angle ACB = 45°. Find angle ADC

Dear Student,

Please find below the solution to the asked query:

We have rhombus ABCD , As :

Here , $\angle$ ACB =  45$°$

In $∆$ ABC  , AB  =  BC  (  As sides of rhombus ABCD )

From base angle theorem we get

$\angle$ ACB = $\angle$ BAC =   45$°$

From angle sum property of triangle we get in $∆$ ABC :

$\angle$ ACB +  $\angle$ BAC  +  $\angle$ ABC  =  180$°$  , Substitute value and get

45$°$ + 45$°$ + $\angle$ ABC  =  180$°$

$\angle$ ABC  = 90$°$

We know in rhombus opposite angles are equal , So

$\angle$ ADC  =  $\angle$ ABC  , So

$\angle$ ADC  =  90$°$                                                         (  Ans )

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