Question

Based on the information on the diagram, what is the measure of angle ADC?​

Answer 1

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°

⇒  $x+x+50= 180$

⇒ $2x+50= 180$

Subtracting both side by 50, then dividing both side by 2

∴ $x= \frac{130}{2}= 65$°

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°

∴ $BDE+EDC+ADC= 180$° (∵sum of straight line= 180°)

⇒ $65+42+ADC= 180$°

⇒$107+ADC= 180$°

Subtracting both side by 107

∴∠ADC= $180-107= 73$°

∴∠ADC= 73°