Question

In the adjoining figure, ED is a chord parallel to the diameter AC of the circle ABCDE. If ∠ CBE = 63 , calculate ∠ DEC.

Answer 1

This question was in my wkst when I was in 9th....

Well anyway, here's the step-by-step answer:

Final Answer:

∠ DEC = 27

Step-by-step explanation:

Given: Circle(O,r), AC (diameter) || ED (chord),  ∠CBE = 63

To find: ∠DEC

Solution: ∠CBE = ∠CAE (as angles subtended by the same arc by a chord are equal)

=> ∠CBE = ∠CAE = 63 --------- 1

Now, in ΔCEA, ∠CEA = 90 ------ 2 (angle subtended by the diameter on the circumference is 90)

Since, ∠CAE + ∠CEA + ∠ACE = 180 (sum of angles of a triangle is 180)

=> 63 + 90 + ∠ACE = 180 (from 1 and 2)

=> ∠ACE = 180 - (63 + 90)

=> ∠ACE = 180 - 153

=> ∠ACE = 27

Now, AC || ED (given).

=> ∠ACE = ∠DEC = 27 (interior opposite angles)

Thus, ∠DEC = 27.

Hope this helps you! :) Please mark as brainliest answer!

Answer 2

Answer:

27°

Step-by-step explanation:

Please mark me as branliest answer