Answer:
73°
Step-by-step explanation:
Given: BD=BE
∠DBE= 50°
∠EAC= 42°
DE//AC and AE=CD
Attach is the new drawn diagram with M point.
∵ we know BD=BE, ∴ ∠BDE=∠BED= x ( taking x as unknown angle)
Remember, sum of triangle= 180°
Now, ∠BDE+∠BDE+∠DBE= 180°
⇒ [tex]x+x+50= 180[/tex]
⇒ [tex]2x+50= 180[/tex]
Subtracting both side by 50, then dividing both side by 2
∴ [tex]x= \frac{130}{2}= 65[/tex]°
We know, ∠MAC= ∠MCA= 42° (∵AM=MC)
Next, ∠EDC=DCA= 42° ( ∵ Alternate interior angle as we know DE//AC )
Now, we have ∠EDC= 42°, ∠BDE= 65°
∴ [tex]BDE+EDC+ADC= 180[/tex]° (∵sum of straight line= 180°)
⇒ [tex]65+42+ADC= 180[/tex]°
⇒[tex]107+ADC= 180[/tex]°
Subtracting both side by 107
∴∠ADC= [tex]180-107= 73[/tex]°
∴∠ADC= 73°
