Question

plz guys help it's urgent​

Answer 1

$\huge\sf\fbox\pink{ANSWER}$

We know that the angles in the same segment of a circle are equal 

From the figure we know that ∠CAD and ∠CBD are in the segment CD

∠CAD=∠CBD=60o

An angle in a semi-circle is a right angle

So we get

∠ADC=90o

Using the angle sum property

∠ACD+∠ADC+∠CAD=180o

By substituting the values

∠ACD+90o+60o=180o

⇒∠ACD=180o−90o−60o

⇒ACD=180o−150o

⇒∠ACD=30o

We know that AC∣∣DE and CD is a transversal 

From the figure we know that ∠ACD and ∠CDE are alternate angles 

So we get

∠CDE=∠ACD=30o

Therefore, ∠CDE=30o   

Answer 2

We know that the angles in the same segment of a circle are equal

From the figure we know that ∠CAD and ∠CBD are in the segment CD

∠CAD=∠CBD=60o

An angle in a semi-circle is a right angle

So we get

∠ADC=90o

Using the angle sum property

∠ACD+∠ADC+∠CAD=180o

By substituting the values

∠ACD+90o+60o=180o

⇒∠ACD=180o−90o−60o

⇒ACD=180o−150o

⇒∠ACD=30o

We know that AC∣∣DE and CD is a transversal

From the figure we know that ∠ACD and ∠CDE are alternate angles

So we get

∠CDE=∠ACD=30o

Therefore, ∠CDE=30o